An easy one, I think.

There are only 3 options to serious consider (there other options are clearly inferior)

• take an f(20) with the 6-sided die
• take an f(20) with the 10-sided die
• take the 12-sided die with the 20-sided die

Is it *obvious* which one is best? Is it close?

Rikachu vs. Rikachu swing die setting

[the start of a post from 2017 that I never got around to finishing] I think the theory of setting swing dice after a loss -- or in any situation when the other person's dice are all known in advance -- is pretty well established, though there can be many subtleties in unusual situations. 

Heck, I have no major objections to the presentation at beatpeopleup.com (wait -- that's not completely true!)

But it's still always hard to know at the very start of a match -- if BOTH players have skill or option dice (let alone "select dice" or "plasma dice", etc) -- what value to set for your swing die. Even the very simplest case -- Bunnies vs. Bunnies (or maybe even better: Rikachu vs. Rikachu) -- requires some thought -- and maybe some game theory!

Rikachu's recipe is 1,1,1,1,Y [Y swing can be set to any size from 1 to 20].

This case is particularly simple -- and maybe even resolvable by hand, since, in a LARGE number of cases, the game is decided on the first roll. If I set my Y to be of size 1, and you set yours to any size greater than 1, then I win outright  outright if you roll 2-5 on that die on the first turn (probability 4/Y); if you roll a number greater than 5 (probability (Y-5)/Y), we'll trade off 1-sided dice until the last turn, when you'll win unless you roll a 1 on your Y-swing (probability (Y-1)/Y)

[though what happens if you roll a 1 on the Y on the first turn and our dice are identical? there are some differences between official rules and the old buttonmen web site -- and I don't know what the buttonweavers web site does --  but, in essence, it's either a tie round and we reroll; or it's simply rerolled without being recorded as a tie. (this is a dead link to a discussion of this point on the old buttonmen web site)

(The only nasty case is when BOTH Y dice are of size 1 and a tie on the coming-out roll is inevitable)

Anyway, leaving the tie aside:if your dice is of size 2-5, I'll win for sure! if your die is of size > 5, and ignoring the case where it rolls a 1,

you have (Y-5)/(Y-1) chance of surviving on the first turn, and then a (Y-1)/Y chance of rolling high enough to nab the win on the last turn... overall, this gives you a (Y-5)/Y chance of winning, so if Y>10, you're in good shape!

Of course, knowing that, maybe I shouldn't set my swing die to Y=1 in the first place! But it wouldn't be THAT hard -- though it's a little more complicated as there are many more possible opening rolls -- to do the same computation for any pair (Y1,Y2) of swing dice, and then figure out the nash equilibrium

what's the best move?

It's alwayslurking's turn. He's up by 12.3 sides.   What attack gives him the best chance of winning? 

[I saved this position five years ago -- I don't completely remember why. In reviewing it, at first, I thought the answer was obvious, but I'm starting to second-guess myself.]

ElihuRoot performed Skill attack using [(4):3,p(6,6):6,(W=7):1] against [g(10):10]; Defender g(10) was captured; Attacker (4) rerolled 3 => 2; Attacker p(6,6) rerolled 6 => 5; Attacker (W=7) rerolled 1 => 7.

Game #3544  •  ElihuRoot (Von Pinn) vs. alwayslurking (Buck)  •  Round #4

UBFC 8

Opponent's turn to attack

(4) p(6,6) (10) (20) (W) Button: Von Pinn Player: ElihuRoot

W/L/T: 1/2/0 (3)  •  Score: 23.5 (-12.3 sides) Dice captured: (20), g(10) (4) 2 p(6,6) 5 (W=7) 7 4 g(8) 8 (12) 4 (X=4)  10  g(10) Dice captured: (20), (10) W/L/T: 2/1/0 (3)  •  Score: 42 (+12.3 sides)

Player: alwayslurking Button: Buck g(8) g(10) (12) (20) (X)

b