which of his dice should I take?
Button Men Game #613905 [MODIFIED]
Tournament Legal challenge, copying communication from game 613499
Skills in this game: X Swing, Speed
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Dirgo (20 20 20 X) Score: 26 (-34.6 sides) Rounds Won/Lost/Tied: 0 / 1 / 0 (Out of 3 wins)
Your Captured Dice: 12-sided die, 4-sided die
| X Swing (with 20 sides) | 20-sided die | |
| 13 | 3 Captured last turn | |
| 8-sided die | 8-sided die | Speed 20-sided die |
| 3 | 4 | 17 |
Button Man: Tamiya (4 8 8 12 z20) Score: 78 (34.6 sides) Rounds Won/Lost/Tied: 1 / 0 / 0
Captured Dice: 20-sided die, 20-sided die, 20-sided die
3 comments:
I can meta-game this one, but this is actually one I know because I do this all the time myself (including probably times when it's not beneficial).
He's up by 34 sides and has 36 sides of dice, so in order to win you have to take all of those. Obviously you'll need to roll higher than 17. If you take the 4 and leave the 3, however, then he can potentially skill attack you if you roll a 20. But if you roll an 18 or 19, you only have to roll higher than a 3. So if you take the 4, your chance of winning is: 2/20*16/20. However, if you take the 3, you add one possibility for successful reroll (20) and take away one on the second reroll (4 is no longer a valid option). So your chance is 3/20*15/20. 2*16 = 32; 3*15 = 45, so the better option is to take the 3.
Ethan
Interesting; it hadn't occurred to me to think ahead to the second re-roll, since surviving the first roll is such a big immediate problem.
I think Ethan's math is wrong, though: If you take the [3/8], you have a 3/20 * 16/20 to win (on the second reroll, you lose on a 1 - 4), or 48/400; whereas if you take the [4/8], you have a 2/20 * 17/20, or 34/400. (So the answer is the same (take the [3/8]), just the numbers are different.
As it turns out, the answer is the same no matter what Anders's middle die is showing: If he has [3/8 8/8 17/20], then your odds of winning if you take the [3/8] drop to 3/20 * 12/20 (or 36/400), but this is still better than the 34/400 if you take the [8/8]. You're only better off leaving the [3/8] if the middle die is a 9 or higher. (Which for me at least is around where it starts seeming intuitive to think about "wait, what about the second re-roll".)
Interesting; it hadn't occurred to me to think ahead to the second re-roll, since surviving the first roll is such a big immediate problem.
I think Ethan's math is wrong, though: If you take the [3/8], you have a 3/20 * 16/20 to win (on the second reroll, you lose on a 1 - 4), or 48/400; whereas if you take the [4/8], you have a 2/20 * 17/20, or 34/400. (So the answer is the same (take the [3/8]), just the numbers are different.
As it turns out, the answer is the same no matter what Anders's middle die is showing: If he has [3/8 8/8 17/20], then your odds of winning if you take the [3/8] drop to 3/20 * 12/20 (or 36/400), but this is still better than the 34/400 if you take the [8/8]. You're only better off leaving the [3/8] if the middle die is a 9 or higher. (Which for me at least is around where it starts seeming intuitive to think about "wait, what about the second re-roll".)
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