- does it make more sense to use my 20-sided die or my 18-sided die?
- does it make more sense to take his die with value 2 or one of the dice with value 4?
For both of these, there are tradeoffs (for example, in #2, the three dice with value 4 threaten only 6 values of my rerolled die (1,2,3,4,8,12) vs. 7 threatened values if he's left with two values of 4 and one value of 2 (1,2,3,4,6,8,10); on the other hand, leaving with him with unrolled dice of value 2 may be preferable on subsequent turns to leaving him with unrolled dice of value 4.
Anyway, there must be a single best answer -- but without doing the explicit calculations, I can't quite see it.
Skills in this game: Reserve, Unique, X Swing, Y Swing
Player: ElihuRoot *Dead Dude* *Fanatic*
Your Button Man: Guillermo (6 10 20 uX uY) Score: 33.5 (6.3 sides) Rounds Won/Lost/Tied: 2 / 2 / 0 (Out of 3 wins)
Your Captured Dice: 4-sided die, 10-sided die
| 20-sided die | Unique X Swing (with 18 sides) | Unique Y Swing (with 1 sides) | 10-sided die | |
| 20 | 13 | 1 | 1 Captured last turn | |
| 4-sided die | 4-sided die | 4-sided die | 4-sided die | |
| 4 | 2 | 4 | 4 |
Button Man: Soja's Guardians (4 4 4 4 4 10 r10 r12) Score: 24 (-6.3 sides) Rounds Won/Lost/Tied: 2 / 2 / 0
Captured Dice: 6-sided die, 10-sided die
2 comments:
I would have thought that the 20-sided die was the obvious choice, since your only chance of winning is taking all the d4s and only losing the d1. The d18 is always going to be safe, and the d20 has less chance of being taken.
I'd take the 2:
(i) If you take the 2, jimmosk is left with 4,4,4, which leaves 6/20 chance that you lose your d20 immediately.
jimmosk rerolls one d4 to get 4,4,?.
Then, assuming you take a 4, jimmosk has 4,?, leaving a 6.5/20 chance.
Finally, you just have to survive the ?, which is then a 2.5/20 chance.
Thus the total cumulative chance of losing your d20 is:
6/20 + 6.5/20*(1 - 6/20) + 2.5/20*(1 - 6.5/20*(1 - 6/20))
which is 62.4%.
(ii) If you take a 4, jimmosk is left with either 4,4,2. That leaves you with 7/20 chance of losing the d20 immediately.
Then jimmosk rerolls a die. If he rerolls the 2, then he has 4,4,?, which is the same situation as above.
Thus, the total chance of losing the d20 is:
7/20 + 6.5/20*(1 - 7/20) + 2.5/20*(1 - 6.5/20*(1 - 7/20))
which is 66.0%.
Wait: you say
>I would have thought that the 20-sided die
>was the obvious choice, since your only
>chance of winning is taking all the d4s
>and only losing the d1.
But can't I afford to lose ONE of the d20 and the d18? I'm already up by 6.3 sides, so if I capture all 16 sides of his, I'm up by 22 sides, minus my 1 sided die, I'm up by 21. That's what led to the question -- does it matter if I risk the 20 sided die FIRST, and -- if I lose it -- then fall back on the 18 sided die? or is it better to risk the 18 sided die first -- with a higher chance of being lost -- but then falling back on the bigger die on the final turn or turns?
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