What should he do? What are his chances of winning?
Player: Zegota, score: 41 (-0.6 sides)
capture dice: 20-sided die, focus X-swing (with 15 sides)
| Dice | 4-sided die | 8-sided die | |
| Value | 4 | 3 | |
| Dice | 4-sided die | 4-sided die | 8-sided die |
| Value | 4 | 1 | 2 |
captured dice: 4-sided die, 20-sided die, focus X-swing (with 10 sides)
here's the filler:
Button Men Game #309173
Tournament #5695: #32
Current Round: Round 3. (organized by bowler190)
Tonase vs. Tonase
Rounds Won/Lost/Tied: 2 / 2 / 0 (Out of 3 wins) (for both of us, obviously)Most recent move:
ElihuRoot is performing a skill attack with a 4-sided die showing 2 and a 8-sided die showing 2, targeting Zegota's 4-sided die showing 4.
The 4-sided die is rerolled and the new value is 1.
The 8-sided die is rerolled and the new value is 2.
ElihuRoot takes Zegota's die.
2 comments:
How about: D8 takes D8.
If you reroll 6,7,8, you have a 7-in-8 chance of winning.
If you reroll 2,3,4, you also have over a 50% chance of winning.
If you reroll a 1, you have about a 50% chance of winning still
If you reroll a 5, I still think it's about 50-50.
How do the stats come out?
that's approximately right:
D8 take D8: 3/8 of time,
he (Zegota) rolls 6,7,8 with 7/8 chance of winning.
1/8 of time, he rerolls a 5 and still has SLIGHTLY more than 50-50 chance of winning (17/32, to be exact! I have to reroll both of my D4 to take him, then his D4 must reroll HIGHER (not equal to) my SMALLER die.
if he rerolls a 3 or a 4, I do best to take his D8 with my D4 with value 4... he then has a 3/4 chance of beating me.
but if he rolls a 2, I actually have a slightly better chance by taking his 4-sided die (23/32).
and, if he rolls a 1, he has slightly LESS than 50% chance of winning, only 3/8 chance, since I capture with my D4 with value 1, and he then has to roll a HIGHER value with his D4 to win.
still, his overall chances are quite good
3/8 * 7/8 + 1/8*17/32 + 2/8*3/4 + 1/8 * 23/32 + 1/8*3/8
= 23/32 overall (I think)
about 72% chance of victory.
I hope it's clear that nothing else could be nearly that good. I don't even think you need to do the computations, it ought to be clear that (A) if Z does capture something with his D8, it ought to be my D8 (B) if he were to decide to capture something with his D4, it would either be
(A) my D4 with value 4, (and I'd have at LEAST a 50% chance of victory if he did this, just by capturing his D8, so this is a bad idea)
or
(B) my D8 (and then, after I took HIS D8, he'd have 3/4 chance of victory 5/8 of the time, and 2/4 chance of victory 1/16 of the time, 1/4 chance of victory 2/16 of the time, and no chance of victory 3/16 of the time... bleah, that's more computation than I needed, the point was this is surely less than the 23/32 overall average the other way, in fact, it's only about 17/32. better than 50% chance, but not nearly as good as 72%
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