Sunday, August 27, 2017

Path of Exile: Ultimate Party Buffs?

Path of Exile is a game that can be played in a group of up to 6 players and has a massive number of different options for how one character can do things to help the other characters in their party. Group buffs, enemy debuffs, specialized roles... The world is your grouping oyster!

And yet right now I feel like I get very little benefit from playing with my friends right now. We've all built characters in order to be able to successfully play alone which means they're all self sufficient. They haven't really put any effort into buffing a group (since it tends to be more expensive skill point wise to buff a group than to just find something to buff yourself) and the efforts put into debuffing the enemies will often come into conflict with each other (curses overwriting each other, elemental equilibriuming away an ally's damage, knockbacks, non-magic finders killing things).

So we started mulling over the idea of creating characters actively designed to work well together. If a character is built knowing they're going to get buffs from friends then they can make tradeoffs as they build their character. For example, if I know someone is going to make some really good curses to put on the enemy then I know I don't have to put any skill points into making my curses better. I don't have to waste skill gems on a curse setup. If I know someone is going to focus on doing a lot of damage then I don't have to worry about taking any damage nodes in the tree at all! Everyone can focus on being tough and doing a couple of good things for the group and actually play together without feeling bad about it.

I'm a little hyped, but now I want to make sure I pick up all the ways to help that I can! So I wanted to go through the list of skills and uniques and stuff to see what the different ways of helping out would be. It's important to not try to take too many helping things and end up squishy but it's entirely possible there are some fairly trivial buffs that people could pick up as long as they know about them. So I want to have a list of broad 'roles' and then a list of extra add-ons that could be picked up.

- AoE damage dealer
- single target damage dealer (for bosses)
- aurabot(s)
- multi-curser
- magic finder
- super tank

- elemental equilibrium (would need to coordinate to use the right element)
- conduit to share power, frenzy, and/or endurance charges
- consecrated ground
- no stun after blocking from Guardian
- speed buff after warcry from Guardian
- armour, energy shield, physical reduction, life regen from Guardian auras
- attack/cast speed, damage, resists from Necro auras
- maim
- blind
- culling strike (@20% from Slayer)
- taunts (double reduction from Champion)
- damage and move speed from Champion
- bleeds buff Bloodlust support gem
- knockback (reverse with unique gloves?)
- stuns/freezes
- hinder
- warcries?
- corpse consumption?
- vaal auras
- frost bomb (cold resist reduction)
- spirited response jewel (rallying cry -> mana regen for party)
- the vigil jewel (vigilant strike fortifies the party)
- dying breath weapon (curse, aura, damage amp) {animate guardian?}
- shaper's seed amulet (health/mana regen aura)
- leer cast hat (damage amp) {animate guardian?}

Enemy damage increases
- Inquisitor (nearby 16% elemental damage)
- Champion (taunted 20% damage)
- intimidate (Champion)
- Warchief (near totem 16% phys/fire damage)
- maim support gem (10-14% physical damage)
- shocks!
- wither (140% chaos damage)

Tuesday, August 22, 2017

Path of Exile: Perma-Freeze Bosses

I have been playing a lot of Path of Exile lately. My current character is running the freezing pulse skill gem because they added a unique jewel that buffs it and I had fun with it years ago. The goal of the build is to do a bunch of cold damage and inflict the 'freeze' debuff on all of the enemies. This means they can't take actions, which means they can't do damage, which means I get to be invincible! Mwahaha!

The theory turns out to be better than the practice, however. I can absolutely crush trash monsters but I've been having trouble with bosses. I've been trying to straddle a line of being able to still deal with bosses that aren't frozen so I've ended up with a mishmash of a build where I have some survivability and some freezability but not really enough of either. I will be getting more of both with more levels (both in terms of getting more passive points in the tree and in terms of leveling up my skill gems) but I'm starting to feel like I need to really go all in on one or the other. Running a bunch of curses and instant leech and the like is fine if enemies aren't frozen but if they are then it's not really doing anything for me and maybe I'll be better off without 4 item slots dedicated to doing all my cursing.

Alternatively maybe I'm better off doing all the cursing and leeching without worrying about freezing at all. If I'm building up to being able to leech tank bosses I can do the same for all the trash too and I'd be better off without all the freeze related points in the tree. At that point I may even be better off just using a different spell entirely!

So I think the way to proceed is to work out what I could do to go all in on freezing. See if I think that'd be good enough to freeze some bosses. If so, great! If not, well, probably start a new dude.

Ok, so, freezing... What are the specific mechanics behind freezing enemies? For our purposes only cold damage can freeze and a hit of cold damage will freeze if two conditions are met:

- The hit is a crit OR an inate 'chance to freeze' roll succeeds.
- The hit does enough damage to freeze the enemy for .3 seconds, which at base means doing 5% of the enemy's max health in cold damage.

The first condition is relatively easy to meet. In my current setup I have a 19% chance to crit, 20% chance to freeze, 20% chance to freeze a chilled enemy, 13% chance to freeze a frostbiten enemy, and somewhere from 0-25% chance to freeze based on distance from my character. So while not every hit will meet this check a significant number of them will. If bosses were getting frozen some but not all of the time I would worry more about working on this condition, but they aren't, so I won't.

The second condition is the one I'm getting stuck on. Having to hit a boss for 5% of their health in order to freeze them actually seems a little silly. If I only need to hit them 20 times in order to kill them I don't think I care that they're not frozen. I can kite and/or use flasks for the 7 seconds it'll take to burn them down! Fortunately damage isn't the only way to work on this condition. You can also work to extend the duration of your freezes so that smaller amounts of damage are good enough to hit the .3 second threshold. If you had 100% freeze duration you'd only need to hit them for 2.5% of their max health. 400% freeze duration would mean you only need to hit them for 1% of their max health. I'm not quite sure that would be good enough, and I really doubt I could get that much freeze duration anyway, but I might as well look into it.

Currently I have 60% increased freeze duration, which is every freeze duration node in the tree. There is one 10% ailment duration node which probably also applies, but I don't have. Other potential sources of freeze duration would be:

- jewels which can add up to 16% freeze duration each
- 20%+ freeze duration from quality on a frostbite gem (and maybe more if my curse nodes impact the quality boost)
- elemental proliferation support gem would be up to ~29% freeze duration (and 20% chance to freeze)
- The Halcyon unique amulet has 30% freeze duration (and 10% chance to freeze, and potentially 80% cold damage)
- Southbound unique gloves have 25% freeze duration
- Rashkaldor's Patience unique amulet had 20% elemental ailment duration

And that is all. The last two unique items don't feel very good while The Halcyon runs over 150 chaos to buy. I do have that much, and I suspect I can flip the amulet back if I don't like it, so possibly that is what I need to do if I'm going forward. I can probably grab jewel sockets to get 3 of those jewels, and I can easily get a quality frostbite gem. I currently need my amulet for life and resists, so switching to The Halcyon hurts my health to the point where I probably need to give up on the Kitava's Thirst 4-curse plan. I also _might_ be able to stretch my tree to get that last 10% ailment node at the assassin start location.

All told I can probably get my freeze duration up to 164% without elemental proliferation and 203% with it. That's almost twice what I'm currently sitting at (303 compared to 160) which almost certainly gets me a little closer to freezing some bosses. That's enough that it's probably worth working on...

On top of that, I can also work on doing more cold damage. With all the freeze duration I can manage I only need to do enough damage to hit for 1.7% of the enemy's max health. I'm still not sure if that is good enough... That's 60 hits to kill them, and I attack almost 3 times per second, so it's probably trivializing a fight that would be lasting 25 seconds otherwise? That's actually a lot of dodging... I don't think I can facetank a lot of these fights for 25 seconds with my current setup, so it is probably worth trying. But let's max out our damage too...

Initially my thinking was that if I'm doing a perma-freeze plan I don't want to be relying on the swings involved in crits. So I've taken the node that makes me do 40% more damage if I've crit in the last 8 seconds. This is way better for consistent damage and it saves me taking crit nodes but it's entirely possible I could be freezing some of the time with crits instead of the current none of the time. At this point I'm really committed to this line I think (I'd want a different bandit reward and probably an entirely different class for critting) but maybe I want to create a different character to do crit freezing pulse...

Anyway, with crits totally abstracted away there are really 4 ways to boost the damage of my spell. I can increase the base cold damage of the spell with flat damage (including leveling the gem itself), I can add to the 'increased damage' multiplier in a variety of ways, I can get extra 'more damage' multipliers, and I can lower the enemy cold resistance.

There are so many ways to change all of those things so I went and built a spreadsheet. It was a little surprising to me in some ways, in particular that a level 4 empower gem isn't really worth using. I suspect that's because of how much flat damage I'm adding to the spell via herald of ice? It means there isn't a red gem worth using which makes me sad... I'm going to have to spend a bunch of chromatics to change my 6 link away from BBGGGR into BBBGGG. (I only have a level 2 empower gem anyway...)

At any rate, here's the support gem ordering for different criteria:

30 cold resist (standard boss), freeze duration - controlled destruction > hypothermia > ice bite > slower projectiles > empower (4) > cold penetration > unbounded ailments > added cold damage > pierce > efficacy > empower (3) > elemental proliferation > iron will > empower (2) > faster projectiles > faster casting > spell echo

30 cold resist (standard boss), DPS - spell echo > controlled destruction > ice bite > hypothermia > faster casting > slower projectiles > empower (4) > cold penetration > added cold damage > pierce > efficacy > empower (3) > iron will > faster projectiles > empower (2) > elemental proliferation = unbounded ailments

85 cold resist (cold boss), freeze duration - controlled destruction > hypothermia > cold penetration > ice bite > slower projectiles > empower (4) > unbounded ailments > added cold damage > pierce > efficacy > empower (3) > elemental proliferation > iron will > empower (2) > faster projectiles > faster casting > spell echo

85 cold resist (cold boss), DPS - spell echo > controlled destruction > ice bite > hypothermia > cold penetration > faster casting > slower projectiles > empower (4) > added cold damage > pierce > efficacy > empower (3) > iron will > faster projectiles > empower (2) > elemental proliferation = unbounded ailments

Basically it seems I have enough spell penetration that unless a boss is overcapped it barely isn't worth using the cold pen gem. This is only true if frost bomb is up, and that's not a given.

The spreadsheet wants me to use slower projectiles, but the spreadsheet don't understand that freezing pulse loses damage the longer it travels so slower projectiles has an invisible less damage multiplier in it. This depends on how close I get to the enemies, and it really hurts my trash clear because the size of my attack is based on how fast it travels. Similarly the faster projectiles damage is better than it seems here (but it still seems quite bad).

Spell echo is the best for doing damage, but it's actively bad at freezing a boss. This means I may want to carry one around to swap in on bosses I can't freeze? I suspect I'd rather have faster casting instead for mobility reasons if I can't freeze the boss? Hard to say.

Ice bite looks good, but that's because it's a way to get frenzy charges. If I can get the charges up then it is worth using. If I can't then it's trash. You get them for killing frozen enemies, which will happen all the time on trash and on boss fights with tons of adds but never on a standalone boss.

I think what I'm ultimately going to want to run is controlled destruction, hypothermia, ice bite, cold penetration, and faster casting. It feels like a good setup for trash with a reasonable shot at freezing most bosses. I can swap in a slower projectiles for the ice bite when I can't keep up the frenzy charges and just get right up in the single boss' face. Either way I do want my colours to be BBBGGG so I should get on that.

Friday, June 30, 2017

Twitch Subscriptions for Affiliates

On Wednesday of this week Twitch rolled out the third stage of their program for getting more income streams for small streamers. The first was the bit system, the second was the game selling system (but the games I play aren't part of that scheme so I haven't really looked into it), and the third is opening up the subscription service, which is arguably the most important option of them all.

Subscriptions allow someone to pay $5, $10, or $25 each month in order to get a few bonuses for chatting on Twitch. Twitch takes a pretty big chunk of that (I had one person sub to me yesterday and my dashboard says I made $1.74, so I guess Twitch takes $3.25, but it could be that Twitch Prime subs are worth less? I don't know!) but it's still a way to set up ostensibly recurring income. Donations (direct through Paypal or via the bit system) are super nice and all but they're very erratic. Someone who is looking to be able to pay rent off of streaming is going to appreciate the consistency of subscription revenue.

There's also the weirdness around Amazon Prime which automatically comes with Twitch Prime which lets the person subscribe for free to one streamer. So it's like your Amazon Prime subscription actually comes with a $1.74 rebate, you just have to have the rebate mailed to someone else. Someone else like me!

As for what the person gets, they get a few things that have never seemed terribly interesting to me but there are a lot of people who get really into them. The first is you get an icon beside your name when chatting in that stream's chat that shows you're a subscriber. Partners can customize that icon and can have different ones for different numbers of consecutive months subscribed; affiliates just get a default star. But it's a way to show in chat that you're someone ponying up to support the streamer, and some people like that, so that's cool. The other thing they get is access to a chat emoticon designed explicitly for the stream. They can use it in any stream chat anywhere on Twitch so if you make a really cool emote then it becomes a form of advertising for your channel. (I've never watched AdmiralBahroo stream, for example, but he has some really sweet emotes that people use in my chat all the time.)

Partners get lots of emotes based on how many subscribers they have. Affiliates get exactly 3. One for each tier of subscription. (But if you have enough subscribers to be eligible for tons of emotes I'm pretty sure you can become a partner too so it's not that big a restriction.)

I didn't do a good job of planning ahead (they did say this was coming in the near future) so I don't even have any emote ideas let alone anything made. You can make changes, though it'll take a couple weeks to get things in or changed, so I really need to keep in mind that it doesn't need to be perfect. Getting something decent implemented quickly is more important than getting the optimal thing done in a year.

So I need to come up with some ideas, and then I need to get 28x28, 56x56, and 112x112 PNGs for those ideas.

Thursday, June 22, 2017

WBC: Expected Laurel Case Studies

During this week's Agricola stream we had a bit of a side discussion going about laurels at WBC based off of my last post. Of particular concern was that I may not be properly considering the time invested in making it to the semis which dovetailed into the idea that even if we can use the butt-hour formula (which determines prize levels) to approximate available laurels that it may not hold across different tournament formats. By this I mean that maybe a single elimination tournament is just more efficient than a heats into semifinal tournament. Or, as Randy suspected, the opposite may be true. Twilight Struggle was the game that was brought up as a particular example. My gut feeling is that Twilight Struggle is an excellent game to play, if you are good at it, because it is a skill intensive game with a ton of laurels on the line. Randy thought that the amount of time you need to invest in a day long tournament (it's 5 3-hour rounds all in one day with a final afterwards) would be a huge problem.

I suspect it would probably be a problem because losing an entire day probably kills off a bunch of other tournaments. But my gut feeling is that that's only a problem for someone who plays other games and would be looking to add another and not something intrinsic to the single elimination format. So it's probably a terrible game for Randy or I to pick up in a quest for Consul, but that someone could build a Consul plan around it. But I don't want to just go on gut feelings, I want to crunch some numbers!

Another game that came up was Advanced Civ. It was brought up as being way too much time for the potential payout and my response was that it was likely true, but only because the formula caps at 6 and that Advanced Civ was probably worth about a 10 because of how many hours get invested and therefore it's a bad play because of formula inefficiency. So I wanted to check into that... Turns out I definitely have egg on my face here because it only has a 5 prize level! Having to sink 16 or 24 hours into a game is a really big investment, especially compared to Stone Age only needing 10 hours. But actually, maybe your odds of earning laurels could be a lot higher? (Keven Youells has earned laurels in it for 14 straight years...)

So I want to crunch some numbers for a few games to see how things line up with a couple assumptions. After that I'll decide if I care enough to go through all of the games or maybe if I'll learn some shortcuts that can be used to make assumptions about the rest of the games? Who knows!

Twilight Struggle

This game is run swiss style, but they play until they have 2 undefeated people and then only those two play in the finals. So it's basically single elimination when it comes to 1st or 2nd, but for 3rd-6th you can keep playing after a loss. I'm going to assume you enjoy the game enough to keep playing with a single loss but will drop out with 2 losses. (Actually, the say they use strength of schedule to determine 3rd-6th, so probably I should assume a loss in one of the first 2 rounds is a drop.) The last couple years have seen attendance swing up barely above the magical 64 number so I'm actually surprised they've been able to finish in only 6 rounds. From the recap they had only 3 undefeated players after 4 rounds last year which really doesn't make sense. That implies only 48 people were really playing but they had 70 sign up. There were also only 2 draws in the whole event, so it isn't like that was eliminating people either. So there must have been quite a few people who showed up, won a round, and dropped. So I'm going to assume there are only 48 people in the tournament even if 70 show up, which will inflate the laurel numbers a little because in reality you could be the person who loses to someone who drops.

(Alternatively it could have gone 70->35->17->8->3 if one of the draws was between undefeated people in round 3. I'm not sure which is more likely to be honest. I should hedge a little and assume more like 54 people show up.)

Here are your potential outcomes, assuming a 50% chance to win each game.

50% - drop after 3 hours (0-1)
25% - drop after 6 hours (1-1)
6.25% - drop after 12 hours (2-2)
6.25% - drop after 15 hours (3-2)
3.125% - make finals
9.375% - make top 7

Twilight Struggle has 5 prizes, so you're looking at...

50% - 3 hours for 0 laurels
25% - 6 hours for 0 laurels
6.25% - 12 hours for 0 laurels
6.25% - 15 hours for 0 laurels
1.5625% - 18 hours for 50 laurels
1.5625% - 18 hours for 30 laurels
1.3393% - 15 hours for 20 laurels1.3393% - 15 hours for 15 laurels
1.3393% - 15 hours for 10 laurels
1.3393% - 15 hours for 5 laurels
1.3393% - 15 hours for 0 laurels

For a total EV of 2.1875 laurels earned for 6.65625 hours invested. Or .32 laurels per hour.

Your odds of winning are not going to be 50%, though. This is where a little bit of art needs to seep into our science. If we're looking at someone who is actively good at the game what are there odds of winning a game? Those odds would need to get worse as you got later in the tournament as the worse players would get removed from the pool. Looking at the laurel list the top player has a massive 443 laurels with second place having 161. There are many people with a significant number of laurels which makes me think this is a very high skill game. I think I want to start our mythical great player off with a 90% chance of winning in round 1 and linearly trend that down to 60% in the finals. That changes the above numbers to:

10% - 3 hours for 0 laurels
14.4% - 6 hours for 0 laurels
4.66% - 12 hours for 0 laurels
9.69% - 15 hours for 0 laurels
16.8% - 18 hours for 50 laurels
11.2% - 18 hours for 30 laurels
6.65% - 15 hours for 20 laurels6.65% - 15 hours for 15 laurels
6.65% - 15 hours for 10 laurels
6.65% - 15 hours for 5 laurels
6.65% - 15 hours for 0 laurels

For a total EV of 15.09 laurels earned for 13.2 hours invested. Or 1.14 laurels per hour. Better, but that actually doesn't feel very good...

Advanced Civilization

This game plays two heats and then advances the top 8 players to a final. Each game is 8 hours in length and you can't leave partway through. They get around 40 players total, so if every player played in both heats you'd be looking at somewhere between 10 and 12 winners. I don't know how likely that is to happen. The recap for last year says they only had 9 people play in both heats, with 28 people in the first heat and 16 in the second heat. So they only had 6 games total, with one guy winning in both heats. Two of the winners didn't even show up for the finals, so they advanced 5 people who hadn't won a game. By the sounds of it, showing up for the finals after playing a decent game advanced you. But two years ago they had 8 games in the 2 heats with one double winner with all winners showing up and a very tight battle for closest 2nd...

To be safe, I think we need to assert that you need a win or a very close second to advance. If that isn't true, and it turns out to be a 'soft' game, then enough of us will show up to make it become true for future years. It seems like games in the heats are often 7 players, but they could be anywhere from 6 to 8.

This means that it's likely that the breakdown for this game is going to be:

1/7 - 8 hours to make finals
6/49 - 16 hours to make finals
36*2/49/8 - 16 hours to advance as a close second (assuming you play both heats and that 2 of 8 2nd placers advance)
55% - 16 hours for 0 laurels

Then once you're in the finals you need to commit another 8 hours for a 1 in 8 chance at each possible result. It's a 5 prize event, so 50-30-20-15-10-5-0-0. The math churns out to be 7.29 laurels for 18.4 hours, or .395 laurels per hour. Better than Twilight Struggle when the games are coin flips!

But Advanced Civ games are _not_ coin flips. There is definitely some randomness, but since there's a guy who laureled 14 years in a row I think it's pretty safe to say that someone who is really good at the game is going to be really good at the game. But how good is really good? Are they going to be 50% to win a heat against 6 other players? More than that? What about their finals odds?

I think I want to give the good player 50% to win a heat, 25% to come a close second. Finals odds I want to be 20-20-20-20-5-5-5-5. Advanced Civ is a game that ends at quasi-random times, especially in a final where people can be playing for best position as opposed to a heat where I wouldn't anticipate a lot of playing for 3rd or 4th.

This puts the EV at 22.2 laurels in 19.5 hours for an overall laurels per hour of 1.14. I swear I didn't cook these numbers... They really do round to the same as Twilight Struggle.

Thurn & Taxis

This game is run with 3 heats of 2 hours each. Winning a heat is good enough to advance to the quarterfinals but if you do particularly well you can earn a bye into the semis. This leads to two different possible plans... You can try to win a single heat and then sit the rest out or you can play every heat in an attempt to earn that bye. If Thurn is the game you care about you definitely want to try to earn that bye but if you're trying to maximize total laurels it likely depends what you could be doing with those time slots.

Last year had 36 people play in 3 heats, 51 people play in 2 heats, and 61 people play in a single heat. That means something like 70 games were played. I believe 4 people got byes to the semis which means 2 wins is not good enough for a bye. I don't know how to track things forward to future years, but I suspect a decent assumption would be that 3 wins is worth a bye to the semis and everyone else has to play the quarters. So my player is going to play at least two heats but only commit to playing the third heat if they have 0 or 2 wins.

1/64 - spend 6 hours to make semis (WWW)
3/64 - spend 6 hours to make quarters (WWL)
3/16 - spend 4 hours to make quarters (WL)
3/16 - spend 4 hours to make quarters (LW)
9/64 - spend 6 hours to make quarters (LLW)
27/64 - spend 6 hours to cry (LLL)

From there it's a bunch of number crunching because of the different number of hours that can be spent on each branch, but my spreadsheet spits out that you expect to earn 1.27 laurels after spending 6.77 hours, for .188 laurels per hour. Which makes T&T a worse use of time than the previous two games when every game is a coin flip! I suspect the reason for this is that no-skill semis are actually a real bad use of time and no-skill quarters are even worse. 94% of people not earning any laurels at all is pretty rough! I guess that's the downside to 150ish player fields compared to 40 player fields!

Anyway, how good can you be at T&T? This is a harder one for me to estimate because I simply don't grok the game at all. It has had repeat winners, I recognize the names of the winners as all being quite good at games, and the laurel list has some big numbers on top so there's definitely skill there. The TrueSkill list on Yucata makes me think it's more random than Stone Age, but still has a pretty high skill component. So I'm going to say our good player wins 45% of heats, 40% of QFs, 35% of SFs, and 30% of Fs.

Swapping in those win rates to my spreadsheet spits out 5.07 laurels in 8.27 hours, for .613 laurels per hour. Much worse than either of the last two games! Is that my being unfair to skill factors in the games, or is it just that the big Euro heat game is not a very good play for laurels? (Heats do get punished by the WBC butt-hour formula, for what it's worth.)


Innovation is a super short single elimination tournament. Heats are scheduled for an hour but it's pretty likely 4 rounds will get compressed into 3 hours. I think I need to keep assuming every round is a full hour though, because sometimes slow people play... At any rate, I'll be considering it to be a mulligan + 6 rounds, with everyone who makes it to the 4th round getting laurels. (The game historically has had 6 people make it that far.) I'm also going to assert that if you win the mulligan you don't show for round 1, but if you lose it then you do.

In coinflip land, this means:

1/4 - out after 2 hours (LL)
1/4 - out after 2 hours (W-L)
1/8 - out after 3 hours (LWL)
1/8 - out after 3 hours (W-WL)
1/16 - out after 4 hours (LWWL)
3/16 - top 6

From there it actually gets a little tricky because of issues with byes/eliminators and that potential extra hour from the mulligan and round 1. Eugh. I'm going to assume the eliminator always loses, which is not true historically so maybe you should bump the numbers up a bit. With that assumption, off to the spreadsheet... (Oh, and Innovation is a trial, so it's only worth 20 laurels for 1st place.)

It pans out to earning 1.5 laurels for an investment of 2.95 hours. This means .508 laurels per hour which is our best coinflip rate so far! I suspect this is because not enough people play so first place shouldn't be worth 20 in a perfect world. So the people who do play get extra value for doing so?

How about a skill factor? Well, one person (Pounder) has made the finals in each of the last 4 years. We've played quite a few times for fun over the years and he routinely smashes me. I beat him once that I can remember (in the finals in 2015, hah!) but other than that I'm not sure I've ever beaten him. There are 7 rounds, so we need 7 win percentages. Round 1 should be the highest number since all the mulligan winners are taking that round off. I feel like I want the finals odds for our great player to be 60, so we'll use a similar scaling backwards thing that we did in Twilight Struggle? With the mulligan round being the same as round 2? So 84%-90%-84%-78%-72%-66%-60%.

Doing that gives us 7.13 laurels in 4.39 hours, or 1.63 laurels per hour. Unsurprisingly the highest coinflip game thus far is also the highest skilled game thus far. Is it fair to say Innovation is as skill intensive as Twilight Struggle?

Vegas Showdown

I want to do at least one more Euro, so let's do one that I think is more random than T&T or Stone Age. The reason I think Vegas Showdown is more random is that you have to pick a strategy pretty early on in the game but the winning strategy can't be known without knowing the order of the card deck. There are certainly still edges that good players will eke out over the course of the game, Showdown isn't on the level of Can't Stop or anything, but I think even the best players are going to win less frequently at this than at some other Euros. (It probably doesn't help that the elimination games are 5 player games.)

There are 3 heats of Vegas Showdown cutting 25 players to the semifinals. The last 2 years have each had 39 games played across the heats so there are likely to be a couple people with a win who don't make the semis. Last year had 7 double winners, leaving 25 more single winners, so 7 winners didn't advance. As such I think you definitely need to play at least 2 heats, and should probably play the third unless you already have at least a first and a second. Heats tend to be 4 player games and this is a 4 prize event.

It ends up being one heck of a spreadsheet, but it churns out 1.89 laurels in 6.21 hours or .303 laurels per hour. Which puts it ahead of Thurn, but behind all of the other games looked at thus far. It feels like games where you need to do better than win a heat to advance are bad deals.

We need to pick some skill numbers for Showdown. I think it'll be fair to pick numbers a little lower than Thurn because Showdown feels more random to me. I'm thinking a 40% chance to win a heat, 30% chance to come second in a heat, 30% chance to win a semi and finals odds of 25%-25%-20%-15%-15% for the different places.

Plugging those numbers in gives us 4.84 laurels in 6.87 hours, or .705 laurels per hour. That doesn't change where it lands relative to the other games.

I am getting very tired, and it turns out to be a fair amount of effort to do individual games. I'm more than happy to discuss methodologies if people disagree with these numbers, but I don't feel like my mind has been changed by looking at these games. Needing to do better than a win in a heat feels really bad to me now. You're getting dinged in the butt-hour formula for having heats but you don't get to save any time by taking heats off. Trials do feel good though, since they're probably heavily overvalued by being worth 20 laurels for a win.

Friday, June 16, 2017

The MVP of WBC

In the last few months my main streaming game has become Blood Bowl. There's a decent computer implementation of the board game (which I have been playing off and on for 18 years) and it turns out I'm pretty good at it and people like to watch good but not perfect play. (It gives them a chance to spot better plays and feel smart!) One of the mechanics of that game is that each team gets assigned a random MVP after a game which is worth a bunch of experience to help level your players. One of my viewers from the pre-Blood Bowl days saw a discussion about the MVP and asked if I'd ever won MVP of the World Boardgaming Championships.

Now, he was being silly, as many Twitch chat people are, but the question has festered in my mind for months. There is an MVP of sorts at WBC. It is definitely not assigned at random, though. Every event at WBC awards points to the top 6 finishers based on size of the event. Sum up all of these laurels and whoever has the biggest number is the MVP. They actually have two such awards. Caesar is awarded to the person who earns the most laurels over a 12 month period, Consul is awarded to the person who earns the most laurels at WBC. They care more about Caesar because they want to encourage people to play in events outside of WBC (a bigger deal when they actually ran a second convention) but I don't much care for play by email tournaments of wargames so for me Consul is the interesting thing.

Looking at the totals needed to be Consul in the last 10 years we see 130, 129, 100, 151, 133, 133, 108, 128, 120, and 156. The most you can get from a single game is 60 and that's for winning one of the 11 biggest events. Available laurels peter off pretty quickly, with second place in a huge event being worth 36 and winning one of the next 12 biggest events being worth 50. Something like 3rd place in a 4 class event (24-53rd biggest events) is only worth 12 laurels. So to get Consul you're looking at needing to win 3 events, or maybe 2 with some other good finishes.

I did come close once, when I earned 99 laurels in 2008. I won a 6 event, won a 3 event, came 4th in a 2 event and 6th in a 3 event. That was good for 3rd place that year (and 16th for Caesar, to show how many points could be earned outside of WBC) with the winner having won 4 different events and an extra 4th place thrown in for fun. I also came 9th in 2012 where I had 2 1sts, a 2nd, and a 6th all in 3 events. That was good for 81 points where first had 133 with 3 wins, 2 seconds, a 4th, and a 6th.

So it's not outside of the realm of possibility that I could have a really good year and come out on top, but it's not actually very likely if I don't make some sort of change. In recent years I've been spending less and less time at WBC actually playing in tournaments or expecting to do well when I do. Moving to New Brunswick meant I both didn't play any games and cared more about hanging out with friends at WBC than playing in events. So while in previous years I may have done things like randomly played a heat of Tigris & Euphrates (in which I somehow came 2nd in 2010) to boost my laurels I wouldn't have done so the last couple years. Which did mean that last year was my first year in 10 where I didn't win a single plaque. I'd averaged 46 laurels per year for my first 9 years; last year I got 2. It felt a little bad. I should be better than that.

Now, I've been playing more games in the last year and in particular I'm hyped about my ability to play a new game for the first time in a long time. The format for Star Wars Rebellion sucks, which has dampened my enthusiasm, but I still have reasonable hopes of being able to win. So maybe I can just use that as my motivation for this year, but I want to think more on trying for Consul. At least think about how to best position oneself for doing so even if I don't end up actually doing it.

There are a couple of variables at work when trying to max out opportunities for laurels. Generally speaking the prize level of an event is based on the hours spent by all players on the event. So if an event takes longer it'll earn you more laurels but cost you more time. If an event has more players it'll earn you more laurels but the competition will be stiffer. These should all even out in the wash so that where you spend your time isn't terribly important... Winning one of those 11 6-prize events is a huge boost, but they should be a large time investment with a small chance of pulling it off.

Stone Age, for example, is one of the 6-prize events. It gets around 160-200 players, has 3 heats, and runs a quarterfinal. If you wanted to put in the best chance at winning the event you're probably looking at playing at least 5 games. (Either play all 3 heats to try to earn a bye through the quarterfinals or play 2 heats to get a win and then win the quarters and semis to make the finals.) So you'd be looking at investing 10 hours to get a smallish chance at the 60 laurels.

Stone Age is actually a fairly skill intensive game I think, and one I'm decent at, so I'd probably give myself a 40% chance at winning a 4-player semi and maybe a 30% chance at winning a 4-player final. So if I asserted I could get a bye I'd be looking at a 12% chance at getting 60 laurels for 10 hours. With some smaller payouts down the line too. Probably not a bad idea.

What might make it a bad idea is when those 10 hours take place. The scheduling game at WBC is not an easy one! The first heat of Stone Age conflicts with History of the World (one of the other 6-prize events) and the single elimination tournament for Innovation (an event I've won in the past). The second heat conflicts with Empire Builder (another 6-prize event), Castles of Burgundy, and Concordia. The third heat conflicts with the single elimination tournament for Star Wars Queen's Gambit (an event I've won in the past). The elimination rounds for Stone Age conflict with all kinds of other semis and finals since they start at 9am Saturday morning.

Which leads to one revelation... Find games that have no conflicts. If the thing that matters is spending time playing games (that you can play through to the finals) then playing games with no conflicts is a good plan. So things that start at 11pm and go past midnight aren't going to have any conflicts and are basically a freeroll. Play Slapshot because it doesn't cost you time you could be spending on a higher payoff event. *sigh*

Certainly one way to gain a big edge in terms of laurels earned is to play a game where you're much better than the average player. Back when Le Havre was an event at WBC I made the finals all 6 times. Even with a smaller prize level than Stone Age, that would be a much better play for me.

The flipside to that is avoid games where you're significantly worse than the average player. My chances of winning a semifinal of Agricola are likely to be in the single digits. They use extra cards that don't ship with the game and with which I have played exactly one game. If I'm trying to earn laurels I'm probably much better off playing Seven Wonders, Love Letter, Scythe, Ra!, and Las Vegas all in the time I'd have to spend playing 3 heats of Agricola. Then the next morning I could play San Juan instead of playing the Agricola semi.

Some events are basically random. If no one is better than average then you just need to understand the game enough to be average and show up. Someone has to win Can't Stop. Why not Zoidberg?

One other thing to consider is advancement conditions. Some events advance plenty of alternates or don't require you to even win a semifinal to make the final. (Top second in a semi has advanced in plenty of lesser attended games over the years.)

Then there's also the fact that prize levels are quantized. Around 50 of the events are going to be at the 2-prize level, but some of those games are going to have significantly more player-hours than others. The ones with fewer player-hours are likely to be more efficient uses of your time than the others. They may only be worth 20 laurels, but if it only takes a couple hours and there aren't many people to compete against, well, it could be a good idea.

I think if this is something I want to do the next step is to go through all the events and estimate the hours it would take to do well, and estimate the chances of actually doing well. Use this to identify a few events to focus on and then build a schedule filling in the gaps with other events that won't have elimination rounds that conflict with the core games.

Thursday, May 18, 2017

World Boardgaming Championships: Beginner Rules

I have been looking forward to this year's World Boardgaming Championships more than I have in a long time. I've been obsessed with a game that came out last year, Star Wars Rebellion, and it got voted in to be a trial. It hits all of my buttons: a two player asymmetric card driven wargame with a fantastic theme. It's long, with small numbers of dice, but it has a lot of intricate details where player skill can make a huge difference. It's like Twilight Struggle, except I get to get in on the ground floor of strategy and tournament results.

They just released the event previews which explain the tournament format in detail. They're running continuous single elimination with adjudication after 3 hours and 45 minutes. That feels too short but maybe my games with Byung take longer than average because we're evenly matched and he's a tad slow. That said, there are plenty of people at WBC who are also slow... On the other hand, I was expecting to have to play 2 and a half full days if they were running 5 hour rounds, so that at least is potentially a welcome change.

Ending in an adjudication is a scary prospect though. How good is the GM at this game? The preview lists a bunch of things he'll look at to decide who wins, and they all make sense, but which things will get the edge in a close game? The proper side to bid on can change depending on how the GM rules in his adjudications and I have no way to access that information right now. This is a little frustrating and curbs my enthusiasm a little bit.

But that's not the worst part. The game comes with a 'first game setup' to help new players ease into the game. There are a _lot_ of great strategic decisions that happen in the initial setup and new players will have no idea how to make those decisions. The game definitely needs to ship with those rules. Unfortunately the default at WBC for every round is going to be using this initial setup. If both players agree they can play the real game, but the default is to play the initial setup.

Now, I think WBC brings in a wide spectrum of players with a wide variety of skills. I think it is important for games at WBC to have demos and to try to accommodate new players. But I also think it's important that a tournament work to test the skills of the players to the utmost. It's a spectrum, for sure, in terms of how much you want to encourage new players versus how much you want to fine tune the games for the experts. I've argued against Agricola using decks that didn't come in the box, for example. I've been against banning cards in Agricola because I think there's value in having people play the game they can buy in a store and not a modded version of it. But the experts don't want to lose to someone with a wood hut extension, and they won that fight. Maybe this is the same sort of thing? But Star Wars Rebellion ships with rules for setting up the game that aren't the initial setup, so I think it's in a different spot on the spectrum. Oh, and the rules for 'First Game Setup' explicitly state 'for future games, use the "Advanced Rules" on page 18'...

I think a fair compromise would be to default the first round to the base game (that's where the people learning the game at the demo are going to be playing anyway) and make the mulligan round and all future rounds default to the advanced game. If two newer players win the first round and meet in the second round and want to base game it up, let them, but forcing experienced players to play the base game just feels awful.

How bad is the initial setup in the base game? I've never played it, so I wanted to dig it out and see...

The advanced setup randomly assigns 3 of 5 systems to the rebels, and 5 of 7 systems to the empire. The base game assigns specific systems, and those systems seem to favour the empire. The rebels don't get to start in Mon Calamari, the empire gets loyalty in both Corellia and Mustafar. It's not an ideal start for the empire, but it isn't one of the disastrous ones either.

The unit mix for each side is the same in either setup, the difference is that they're preset in the base game and you get to make decisions that shape your future plans in the advanced game. The base game spreads out the empire units, which in my experience with the advanced game is a horrible plan. You don't have enough actions to move 6 different forces around, and the rebels have enough units to pick off 1/6th of your forces in any given spot. Spreading out just gives them more targets without really giving you more options.

On the other hand, the reason the empire needs to worry is the rebels are supposed to see the initial setup and then pick any space on the board to deploy their smaller force. You get to split between the rebel base and any system, and then the rebels get to take the first action in the game so they can attack the empire in any poorly defended spot. In the base game they force the rebels to split up their forces in a truly terrible manner, and they force them to be placed away from ANY of the 6 empire spaces.

How awful is the split? Well, my experience has shown that the rebels only really care about their fighters and their speeders. They start with 2 of each and you want to save them for a crucial time because they're very useful and hard to come by. The basic setup splits them down the middle with 1 x-wing, 1 y-wing, and 1 speeder in each of the two spots. You can't realistically get them back together to make use of them without wasting an action on turn 1. And that action will only consolidate them into the rebel base, not somewhere useful where they can do anything to harass the empire!

The worst part is they start those units in one of the 3 rebel systems, so the empire now has a single place to go in order to both remove rebels builds and to destroy rebel forces. There aren't many rebel units ever (they start with only 14 bits and probably build 4-6 every 2 turns), so having 8 of them start in a vulnerable, worthless space is terrible!

Our feeling is the rebels are the better side, but everything about the base game setup screams advantage for the empire.

Maybe there's some play in the base game that I'm missing? Maybe saving the time from doing an initial setup and by restricting opening strategies is worth playing a worse game? Maybe I'll calm down in time? But right now, after looking at the base setup, I am not really very keen on playing the game. and by extension, not nearly as excited about WBC as I was earlier in the week.

Saturday, May 06, 2017

Twitch Affiliate

Last week I had a viewer ask me if I was hoping to be part of the Twitch Affiliate program. I didn't even know what that was but told them I'd take a look at it when I got a chance. Well, it turned out I'd already been invited to take part in it and just hadn't noticed the email or notification. Their criteria for who they'd invite is public but they were going to be rolling invites out in waves so while I certainly qualified it wasn't clear if I'd have gotten in yet or not. It turns out I was invited the first day they started inviting people so I'm taking that to mean I'm doing pretty well when it comes to not being a partner.

For those who may not know, until last week there were two types of streamers on Twitch. Partnered streamers (who have a bunch of monetization schemes available to them like monthly subscriptions and ad revenue) and everyone else. Becoming partner requires filling in an application and meeting some nebulous requirements. Now there's a tier in the middle that you can autoqualify for and that brings some of the perks of being a partner and doesn't require a live person to go over your application. It feels like a win-win for both Twitch and up and coming streamers!

Anyway, the requirements to qualify for affiliate are 50 followers, 500 minutes broadcast in the last month, 7 different days live in the last month, and an average of 3 people watching at a time. In April I streamed for 10262 minutes across 22 days with 22 average viewers and I have 899 followers. That's a little more than the minimum!

What does being an affiliate get me? For now, not actually a whole lot. I get access to the bit cheering system and higher priority for getting quality options as their servers allow. The priority thing actually doesn't really change anything because they already had a priority system based on number of current viewers. I guess it'll help if I stream a game where I get significantly below my average number of viewers (those few people might get quality options now when they otherwise wouldn't) but it's really not a big deal.

The bit cheering system is an interesting one. It's something Twitch added a while ago as a way to protect streamers from chargeback fees on various online money sites like PayPal. Basically Twitch will sell people bits and they can use those bits to tip streamers. Streamers then get a payout each month based on the bits they've been given and if someone uses a stolen credit card to buy bits then Twitch will eat the loss instead of the streamer. In return for that protection Twitch takes a significant chunk of the revenue upfront. (A bit is worth 1 cent but Twitch charges you $1.40 for 100 bits. They have bulk discounts too, but they're always taking a pretty big cut.) Now, PayPal also takes a cut of donations too (2.9% + .30), but it seems that fraud notwithstanding it's actually worse for me to get paid via bits than via PayPal. Especially since affiliates need to wait 60 days from the end of a month to get paid for bits. And that they have to pay a fee to get that payment (2% to PayPal is the option I chose)! And if I understand the tax forms they made me fill out in order to sign up the US Government is going to take 30% hostage as well!

There are other ways to get bits than buying them from Twitch, though. People can earn bits by watching ads, apparently, and they can be found in loot crates that they've started giving out in various ways. And obviously no one is going to complain about addition potential revenue streams! It also helps that it's fully integrated to the Twitch system so it's much easier for a viewer to buy some bits and then spread them around when they feel like it instead of having to log in to PayPal or whatever. Getting access to the bit system is definitely a plus!

Coming Soon (tm) they'll be adding on subscriptions, game sales, and ad revenue to Twitch Affiliates, all of which are more exciting to me than cheering was. Subscriptions are a consistent source of revenue and getting even a single channel emote would be really cool. Ad revenue would be nice since Twitch plays ads on my stream without my ability to remove them so getting some recompense for that would be good. And game sales... I know for a fact I'm already selling games to people. Last year I got people back into World of Warcraft from watching me play and I know people have bought things like Factorio and Blood Bowl II because of seeing me play the game and thinking they might like it. So getting a 5% cut of those sales (and making it easier for people to be able to buy the games) just sounds fantastic to me.

So things are looking up. Hopefully I can manage to stay unglutened and put in a string of good streaming days and see where things go from here.

Monday, May 01, 2017

Blood Bowl: How Bad is Stab?

A couple weeks ago I played against a Dark Elf opponent that was running two assassins on a relatively unleveled team. This means they chose to take the assassin over other positionals, which means they must have valued them pretty highly. Twitch chat was not very charitable to the skill level of my opponent, and the assassins actually accomplished basically nothing. They spent a lot of time intentionally standing beside my guys and then getting hit for it with their 7 armour, but that held up just fine.

It got me wondering... Should I have been able to just get free SPP for killing them? Should he have been able to hurt any of my guys first? Is conventional wisdom about how bad they are correct or should I be trying them out? Setting up with 2 of them on the line, making stabs, and then blocking away anyone who didn't get stabbed feels at least worth investigating. (My opponent tried this, but I was playing necro and the players he was stabbing had 9 armour and stand firm so blocking them away couldn't happen.) What are the odds here?

Nothing Stun KO Cas
7 AV 58% 24% 10% 7%
8 AV 72% 16% 7% 5%
9 AV 83% 10% 4% 3%

TO Push Down Stun KO Cas
7 AV 3% 22% 44% 18% 8% 5%
8 AV 3% 22% 54% 12% 5% 3%
9 AV 3% 22% 63% 7% 3% 2%

TO Push Down Stun KO Cas
7 AV 11% 33% 32% 14% 6% 4%
8 AV 11% 33% 40% 9% 4% 3%
9 AV 11% 33% 46% 5% 2% 2%

TO Push Down Stun KO Cas
7 AV 11% 58% 18% 7% 3% 2%
8 AV 11% 58% 22% 5% 2% 1%
9 AV 11% 58% 25% 3% 1% 1%

The first table is for stab against the 3 likely armour values the target is apt to have. The next one is the odds for a 2 die block with block against someone without block. The next one is the odds for a 2 die block without block against someone with block. The last one is the odds for a 2 die block without block against someone with both block and dodge.

The first thing to point out is that there is no downside to the stab. Throwing a block without block has an 11 percent chance of knocking yourself down. You can reroll it, of course, but burning up rerolls on opening line blocks feels really bad. Especially when the upside of throwing the block is only a 4% chance of removal!

Then there's the fact that even if you give up a 2 die block back after failing a stab they are only 13% to remove you back. If you're stabbing a 7 AV person that means the stabber has the advantage. Otherwise you're less likely to hurt them as you are to be hurt back, so you really need the followup block from a friend trying for a push to free you up. Hitting a flesh golem with an assassin is not a good play.

That all said... A 13% chance to be removed back is actually a really big deal. And that's assuming they don't have mighty blow, which, now that we mention it...

TO Push Down Stun KO Cas
7 AV 3% 22% 31% 20% 13% 11%
8 AV 3% 22% 44% 15% 9% 8%
9 AV 3% 22% 54% 10% 6% 5%

Now we're up to a 23% chance of being removed! Those are the sorts of numbers I'm talking about. Mighty blow really lets you murder the 7 AV dudes with no skills. No wonder my rats keep dying...

The next thing I notice is just how hard it is to hurt someone with block and dodge with a regular hit. Even with 7 armour you're only getting removed on 5% of hits. 5% of regular hits, anyway. Throw on tackle and mighty blow and things get a lot scarier. But it's not like a Dark Elf team is going to have many (or any) players with those skills. If we're trying to kill a gutter runner or a skink or something then maybe the assassin is the way to go. 17% instead of 5% is a pretty big change!

My feeling now after looking at things a little is that blitzing anyone except for a low armour dodgy dude is a mistake with an assassin. This means they have to start in contact on the start of your turn to get a hit off, which is very dangerous for a 7 armour dude with no defensive skills. Using them against enemies on the line feels pretty good though. Take a free armour roll, then hit them with a regular block to push them away (or knock them down) afterwards. If you knock them down beside the assassin then next turn they have to dodge away or give you another stab...

It also feels like they just aren't likely enough to knock anyone down to justify using them on the ball carrier if you have an actual ball removal player. Tackle, wrestle, strip ball... These are all better tools than the assassin. But those all require a lot of levels; the assassin comes straight out of the box with stab.

Another downside is the stab doesn't earn any experience, so the assassin is a removal tool that doesn't level through removals! Can you feed them touchdowns to level them up? All the players on a Dark Elf team want to level up through touchdowns, can you justify feeding the spp onto the assassin?

And really, that's what it comes down to... Assassins are expensive players on a team full of expensive players. They're pretty much the squishiest player in the game, too, since they have only 7 AV and no defensive skills. Even goblins, which have stunty, start with dodge, so they're harder to hurt. Harder to hurt for everyone but an assassin, anyway!

So I feel like I'd maybe want an assassin (or two!) against some specific teams but very much not against others.

Good: Skaven, High Elf, Brettonian, Wood Elf, Lizardman, Norse, Khemri
Ok: Human, Dark Elf, Undead, Chaos Dwarves
Bad: Orc, Dwarf, Chaos, Necromantic, Nurgle

Hmm... Looking at it there are actually 7 of 16 teams where I'd probably want an assassin and only really 5 where they'd be a real detriment. Of course on the champion ladder it turns out that the bottom group there contains a lot of the most played teams. Orcs are #1 by a large margin, with Chaos and Chaos Dwarves as the next two. Those 5 bad teams represent 40% of all games played and that really makes me question wanting to play assassins on the ladder.

But in a league? That's more tempting. Especially if the league enforces some kind of race parity like the NWFL league I played on FumBBL did.

Of course you could just be looking at having your expensive defenseless 7 AV player die in the first game...

Thursday, April 06, 2017

Blood Bowl Puzzle

An interesting situation cropped up at the end of a recent Blood Bowl game, and I wanted to look into it in more detail while not being under a 3 minute timer to make all of my moves in a turn. In some senses it's a very straightforward position and in other senses there's a lot of things going on that need to be considered. I thought it might be interesting to provide the situation as a puzzle and let people decide what they would do and then go through all of the things to consider in another post.

The Blood Bowl 2 interface is pretty good for watching things live, but pretty sketchy for easily seeing things at a glance for people who aren't used to it, so I'll explain what's going on in this picture first.

This is turn 16 of a game where we're down 2-1. We're a brand new Necromantic team, dressed in pink, and we're playing against Dwarves. We have possession of the ball, in the hands of a werewolf who is 8 spaces from the endzone (indicated by the blue pillar of light). Werewolves have an 8/3/3/8 statline and their only relevant skill is frenzy. We don't have any rerolls and the only thing we care about is maximizing our odds of scoring a touchdown to tie the game. No other player on our team can reach the endzone and there aren't enough players on the field to set up any crazy chain push plays (I don't think, anyway!).

The other players we have access to are 2 flesh golems (4/4/2/9), 3 zombies (4/3/2/8), and a wight (6/3/3/8 block). Our second wight is lying on the ground beside the ball carrier but unfortunately he is stunned. There are not many dwarves left in play, but the ones that exist are in annoying positions. All dwarves have 3 strength and all of them have block except for the one hiding behind the flesh golem in the upper left hand corner. The remaining dwarves are marked one on the werewolf, one on the second flesh golem, and one on a zombie. We have 2 free zombies and a free wight, all a fair ways behind the play.

What is your plan for the turn?