Monday, January 25, 2016

Blood from stones

OK, i's turn. Can he win? it's definitely not likely, but there's one move that gives him a small chance and another move that gives him an even smaller chance, assuming I don't deliberately play suboptimal moves.

Game #9707  •  ElihuRoot (Foxlady) vs. irilyth (EDG)  •  Round #3
reverse
Opponent's turn to attack


fo(X) t(4) z(6,6) m(12) (Y)?
Button: Foxlady
Player: ElihuRoot
W/L/T: 1/1/0 (3)  •  Score: 42.5 (+10.3 sides)
Dice captured: (20), I(10), I(8)
fo(X=4)
2
t(4)
1
(Y=1)?
1
3
I(6)
2
(X=4)
 3 
I(8)
Dice captured: z(6,6), m(10)
W/L/T: 1/1/0 (3)  •  Score: 27 (-10.3 sides)
Player: irilyth
Button: EDG
I(6) I(8) I(10) (20) (X)

Basic point, not a hard puzzle

But it's a nice explicit instantiation of a basic concept. blackshadowshide is almost certain to win thie round, no matter what. But are his chances better if he takes the 4-sided die or the 8-sided die? Or does it not matter?

Of course, 16 times out of 20, it doesn't matter and he takes them both... but the other 20% of the time, I'll get a counterattack and will win if I manage to reroll a 1. If I am rerolling the 4-sided die, that will happen one time in ..., well four, but if it's the 8-sided die it's only one time in 8. So I wind up with a 5% chance of winning if I can reroll the d4, but only a 2.5% chance of winning if I reroll the d8. Again, I've likely lost no matter what, but why give your opponent an extra 2.5% chance of winning?

Game #2032  •  ElihuRoot (Yuranosuke) vs. blackshadowshade (Coil)  •  Round #4
New games galore for people to reject!
Opponent's turn to attack


(4) (8) (12) f(12) (X)
Button: Yuranosuke
Player: ElihuRoot
W/L/T: 2/1/0 (3)  •  Score: 22 (+2.7 sides)
Dice captured: (12), (V=6), p(4)
(4)
4
(8)
4
1
p(20)
13
(20)
 2 
p(4)
Dice captured: (12), f(12), (X=4)
W/L/T: 1/2/0 (3)  •  Score: 18 (-2.7 sides)
Button: Coil
p(4) (12) p(20) (20) (V)