quick computation

It's not deep, but this sort of computation comes up all the time and I wonder if there's a shortcut.

I have to capture the (8) -- and I want to maximize my chances of being able to capture the (20) on a subsequent turn -- but which die should I use?  ONE die choice  is obviously wrong, I didn't have to do the math to know that -- but the other two seemed pretty close.  I did do the math and discovered about a 4% difference between them, maybe that's too close to tell by general principles without crunching the numbers -- but one is a bit above 50% and the other a bit below.

not deep, but I was mildly surprised when I did the computation

I have four possible attacks. One of them is obviously suboptimal, but the others all give roughly similar chances of winning. Or do they? Which one is best?

Priorities

It's AD's turn. Which move(s) will maximize his chance of winning? Which move(s) will maximize his chance of not losing?

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

Subtle poison problem

 I have two options here [as far as I can see, at least]: If I eat the poision, I must also capture the (10) to have a chance of winning.  But if I take the (4) and manage to avoid eating the poison, I can win. I think it's clear that if I take the (4), I should do so with the (6).  But is that the best move?

If I eat the poison first, I have about a 70% chance of forcing the (10) to reroll. But that doesn't gurantee success, especially if I  end the round with my p(12) uneaten.

I know what I decided to do, but I didn't work out the details carefully. What do you think?

do you see a better move?

I'm in pretty good shape here, but i. still has a few low-probability ways to snatch the victory.
What's his best option?

What's his best chance?

What has to happen for Blargh to win? What's the best strategy to make it happen?

small math problem

I should have done the math to see which option is better -- rerolling the 20-sided die will eliminate the (10) and has an 80% chance of surviving for the final reroll [though there's a 1/20 chance of rolling a 5 and possibly having both 4-sided dice reroll higher than 2, etc].

But capturing with the (8) has a 50% chance of rerolling out of capture range for a sure victory! Even if not, the (20) will be able to capture on the next round with at least a 50% chance -- probably substantially better than that -- of rolling out of danger. And it's so cool to leave the (20) so low!

Still, I really should have worked it out in detail to know for sure which option is better.

Nala's choice

This came about in a tournament in which the objective is to maximize one's score, not necessarily win the game; of course, Nala's AI wasn't doing that, anyway.

Anyway, Nala has an interesting decision here.  Is it better to capture with the 8-sided die (and if so, which die should she capture?)  Or to capture with the mood-swing die and who knows what may happen?

And -- given that I'm playing in a tournament in which all I care about is my total score, I might prefer her to reroll the  mood-swing. If I lose the round, fine, I have more chances to play rounds in which I'm able to keep my f(20); and if I win the round, I might capture a mood-swing with more than 3-sides.

*very* basic problem

i'm not even going to ask the question, it's just a simple illustration of a common situation.

n. has to take both my dice without losing either of his own, so (A) he can't leave both my X=4 uncaptured and his X=4 unrolled. So my X=4 must be taken.

On the other hand, if he takes it with his own X=4, he has a 50% chance of rolling it into range of my sf(4), whereas if he takes it with his (20), he has only a 10% chance of rolling it into range of my sf(4), and another 5% chance of  rolling 2 and not being able to make a second attack. So one way he loses 50% of the time, the other way, only 15%.

b

gaining initiative

Yes, I'm going use my focus dice to gain initiative -- but is it really obvious what the best way to do it is? And what my first attack should be? [for the record, I sort of think I made a mistake with my first attack in the actual game]

Is this subtle? I don't want to do the math.

I have four possible attacks here. *probably* I should use the #(8), as I really have to get the 10-sided die to reroll to have any chance of victory -- but should I take the 4-sided die or the p(6,6)?
I can afford to lose one of my dice if I capture all of his, or even *both* of my dive do long as I capture the 10-sided die but NOT the poison.