Is the gain illusory? is it microscopic?
Viewing Game #696251
Tournament Legal challenge, copying communication from game 695958
This game was last modified on Thu May 13, 2010 12:05:02
* Next Turn * Player: Limax *Wombat* *Is a MAN* *Fanatic* * Next Turn *
Button Man: Iago Score: 28 (-20 sides) Rounds Won/Lost/Tied: 1 / 1 / 1 (out of 3 round(s))
Captured Dice: 10-sided die
| Dice | 20-sided die | X Swing (with 16 sides) | ||
| Value | 10 | 2 | ||
| Dice | 6-sided die | 6-sided die | 20-sided die | 4-sided die |
| Value | 6 | 5 | 11 | 4 |
Button Man: Tuxedo Mask Score: 58 (20 sides) Rounds Won/Lost/Tied: 1 / 1 / 1
Captured Dice: 20-sided die, 20-sided die
2 comments:
It's not illusory, but it's microscopic. Limax's [16] will get taken, so even to eke out a tie will require L to take all of Elihu's dice.
Just to make the math tractable, assume Elihu's dice always reroll to the same value they had previously.
If L captures the [6]-showing-5, that ekeing happens 7 times out of 20, then 13 times out of 20, then 16 times out of 20. Total chance of survival (7/20)*(13/20)*(16/20) = 18.2%
If L captures the [6]-showing-6, that ekeing happens 6 times out of 20, then 14 times out of 20, then 16 times out of 20. Total chance of survival (6/20)*(14/20)*(16/20) = 16.8%
Maximize your chances by taking the 5.
Right, your numbers are a bit off because of your simplification, but the general trend is right.
If you take the die with value 6, the exact chance of success is 14.21%, but if you take the die with value 5, the chance of success is 16.23%. [and, for comparison,
if you take the 4-sided die, the chance of success is 15.13% -- suboptimal, but still better than taking the die with value 6 !]
Only 2% [ok, 2.02%], but you might as well have the extra chance of winning, no? That's more than the house advantage in craps and it does add up.
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