Fun math fact

I'm prepared to believe there are some interesting decisions when playing with Bunnies, though I'm not sure I've can remember any. Maybe choosing the swing die on the first round, before seeing one's opponents swing die might sometimes be interesting.

But I do think this sort of thing is mathematically sort of cool, if not a deep decision problem: in the picture below,  J. is forced to take my p20 and then I need to sweep his remaining dice. I can afford to lose either one of my remaining dice, but not both. I could either start with the d12 and then switch to the d6 if the d12 is captured, or start with the d6 and switch to the d12 if the d6 is captured. Does it matter which one I start with?

Can you generalize the result? Can you give a good intuition to back up the computation?

Game #8952  •  ElihuRoot (Coil) vs. Jota (Bunnies)  •  Round #2

UBFC 73

Opponent's turn to attack

p(4) (12) p(20) (20) (V) Button: Coil Player: ElihuRoot

W/L/T: 1/0/0 (3)  •  Score: 9 (-7 sides) Dice captured: (X=19), (1) (12) 7 p(20) 3 (V=6) 5 1 (1) 1 (1) 1 (1)  1  (1) Dice captured: (20), p(4) W/L/T: 0/1/0 (3)  •  Score: 19.5 (+7 sides)

Player: Jota Button: Bunnies (1) (1) (1) (1) (X)

Have I mentined how much I like Crab?

Crab is one of my favorite buttonmen ever. Not just because she often wins, but the decisions and gambits those f20 lead to are just delicious -- they are what buttonmen is all about!

I even like some of the really tough situations she brings -- like this one. I can't keep mcculloch from getting initiative, is it even worth trying? I'd like to keep my f20 showing 19 safe,
but that's not possible, if I only use by f20 with 11 to get initiative, he can win it back with his f6 and I'm dead... even if I could try to use both dice to get initiative, he'd still take it from me and I'd just have two d20s with value 1. It's hopeless, right?

Which makes more sense?

• capture g.'s largest die (12 sides), showing the largest value( 7) at the cost of having to reroll my only die with value greater than 4  or
• keep my second or keep my second- largest die (10 sides) with value 8 safe for at least one more turn while  rerolling my d12 

Game #7401  •  ElihuRoot (Mirumoto) vs. glassonion (Crab)  •  Round #5

Your turn to attack

f(6) (10) f(10) (12) (20) Button: Mirumoto Player: ElihuRoot

W/L/T: 2/2/0 (3)  •  Score: 54 (+6 sides) Dice captured: f(20), f(20) f(6) 4 f(10) 8 (12) 4 (10)  6  2 (8) 2 (10) 7 (12) Dice captured: (20), (10) W/L/T: 2/2/0 (3)  •  Score: 45 (-6 sides)

Player: glassonion Button: Crab (8) (10) (12) f(20) f(20)

choosing reserve dice

In a 3-round game of Sadakuro  [f(4) f(6) f(8) f(10) (12)] vs Sapphire [(6) (10) (12) (12) r(8) r(8) r(10) r(12)], Sadakuro is almost certain to win the first round and has an excellent chance of winning the second round, regardless of the reserve die Sapphire chooses. So, as is so often the case in non-reserve vs. reserve-die games, Sapphire finds himself having to win 3 in a row. Even with the 5-against-6 dice matchup at the end, Sadakuro can be pretty sure of getting the initiative.  Bearing all that in mind, which reserve dice should Sapphire choose to have the best chance? or does it not matter much?

I have an opinion, but I am not completely sure I'm right. I'll wait to hear other comments, if any, before posting it.

submitted puzzle by Jim M.

Which die should you capture first to maximize your chance of winnng?

I haven't thought long enough about this to have a strong opinion, but it looked like it might be subtle to compute -- prove me wrong!

Why shouldn't D. trip the shadow die? why shouldn't D trip the poison die?  which is more dangerous?

Game #1405  •  ElihuRoot (Mushu) vs. Devious (slamkrypare)  •  Round #3

slamkrypare practice!

Opponent's turn to attack

m(U) sH(U) po(R) k(10) Button: Mushu Player: ElihuRoot

W/L/T: 2/0/0 (3)  •  Score: 10 (-12 sides) Dice captured: z(12), (10) sH(U=8) 5 po(R=16) 6 1 t(1) 2 (10) 1 (Y=1)  6  (10) Dice captured: k(10), m(12) W/L/T: 0/2/0 (3)  •  Score: 28 (+12 sides)

Player: Devious Button: slamkrypare t(1) (10) (10) z(12) (Y)

I hate decisions like these.

Well, no, I actually kind of like them, but I hate working out the math.

• option 1: take the c(X=15) now before it rolls out of reach; it's the only single die g. can retain and win. I'll still need to capture either the 10-sided die or both of the 6-sided dice, but that's relatively doable.
• option 2: take the 6-sided die with value 1 now. My 12-sided die will stay safe another turn and I need only capture the 15-sided die and either one of the other two.

I know what I did, and I know, in principle, how to work out the math if I stopped to think. But who wants to do that?

(4) g(4) g(6) (12) (X) Button: Cass Player: ElihuRoot

W/L/T: 1/1/0 (3)  •  Score: 22 (-4.3 sides) Dice captured: (12) (4) 1 (12) 7 (X=4) 2 1 (6) 6 c(6) 6 (10) 5 c(X=15) Dice captured: g(4), g(6) W/L/T: 1/1/0 (3)  •  Score: 28.5 (+4.3 sides)

Player: glassonion

Button: Pikathulhu

(6) c(6) (10) (12) c(X)

Queen's Gambit

I'm almost certainly dead here. Do I have any chance at all? I think there are only two moves that
keep any mathematical chance of me winning alive.

Game #2400  •  ElihuRoot (Nimue) vs. eksortso (Guenever)  •  Round #3

Random Buttonlords (really) (with a reverse)

Your turn to attack

(4) (6) s(12) (20) (X) Button: Nimue Player: ElihuRoot

W/L/T: 1/1/0 (3)  •  Score: 23 (-18.3 sides) Dice captured: (12) (4) 4 (6) 5 s(12) 11 (X=12)  10  1 (6) 5 s(8) 9 (10) 5 (X=13) Dice captured: (20), (X=12) W/L/T: 1/1/0 (3)  •  Score: 50.5 (+18.3 sides)

Player: eksortso Button: Guenever (6) s(8) (10) (12) (X)

Do I take the 10-sided die with my d8? or with my d4  &  s4? or just with the s4? That last one seems majorized by using both the d4 and s4, so we can ignore it -- and PROBABLY, it makes more sense to reroll my d8 in the 50-50 chance of rolling out of range of tavella's remaining dice.

But another option would be to take t.'s d6 with my s4, keeping my 8-sided die safe for another turn with at least a 70% chane of being able to take the d10 on the next turn, guaranteeing at least a tie.

Game #2633  •  ElihuRoot (Tiffany) vs. tavella (Cesare)  •  Round #5

Your turn to attack

(4) s(8) (8) (10) s(X) Button: Tiffany Player: ElihuRoot

W/L/T: 2/2/0 (3)  •  Score: 28 (0 sides) Dice captured: (10/20=10), (10) (4) 1 (8) 6 s(X=4) 3 s(8)  2  3 (4/10=4) 3 (6/10=6) 4 (10/12=10) Dice captured: (10), s(8) W/L/T: 2/2/0 (3)  •  Score: 28 (0 sides)

Player: tavella Button: Cesare (10) (4/10) (6/10) (10/12) (10/20)

Chat:

Default AttackPower AttackSkill AttackShadow AttackSURRENDER!?

Die skills in this game: Shadowi

What are sansibaman's chances of pulling this off?

What's the best move?

There are only three possible attacks, so this isn't too hard to figure out by brute force -- but can you see it quickly?

ElihuRoot performed Power attack using [(X=4):4] against [(12):3]; Defender (12) was captured; Attacker (X=4) rerolled 4 => 1.

Game #3311  •  ElihuRoot (Buddy) vs. sansibaman (Kith)  •  Round #5

Opponent's turn to attack

s(6) (10) s(20) (20) (X) Button: Buddy Player: ElihuRoot

W/L/T: 2/2/0 (3)  •  Score: 53 (+9.3 sides) Dice captured: (X=18), (8), (12) s(6) 4 s(20) 18 (X=4) 1 1 (6) 12 (12)  3  (12) Dice captured: (10), (20) W/L/T: 2/2/0 (3)  •  Score: 39 (-9.3 sides)

Player: sansibaman Button: Kith (6) (8) (12) (12) (X)