the two choices are:
- take her 20-sider now, don't allow it to roll again!
- don't reroll your own 20-sider, what are you, crazy? use your 6-sided die, leading to two subchoices:
- take the 12-sided die, you want it to have a chance of rerolling high?
- take the 4-sided die, 5 times out of 6 he'll have to reroll his 20-sided die and you'll have a very good chance it will reroll 18 or less, with the 12 sided die stuck at value 1.
I think the move one chooses instinctively in this situation says a lot about the sort of person you are -- but what does that even mean? And are these options really as close as I'm implying?
Button Men Game #717790
Skills in this game: Twin, Option, Shadow, X Swing
2 comments:
Since you need to take all of her dice to win, using the six-sider now seems to be a better option: the chances of one of the 20-siders rolling badly for you are higher if you roll yours now than if she rolls hers on her next move, and your chances of taking the last two dice with your 20-sider are better than doing the same with the six-sider.
As for which die to take, taking the 12-sider probably guarantees the 20-sider being rerolled, since that move seems to offer better advantages to her (5% chance of guaranteed win, 5% chance likely win, and only 5% chance of situation getting worse vs. 25% chance of situation getting worse, 50% chance of improving odds of winning 5-10%) if she even has the option to reroll the four-sider. If you take the 4-sider, there's a good chance she'll reroll the 12-sider if she can, since that move can't make her situation worse and probably improves her chances more than rerolling the 20-sider would.
So, without actually doing the calculations on most of the possibilities, my instincts say taking the 12-sider with your 6-sider looks like your best move.
In fact, doing the complete calculations show 3 options, all very similar [and the one you chose is the one in the middle]:
Best: take the d4 with your d6, chance of winning the game: 82.70833333333333
Next best: take d12 with your d6, chance of winning the game: 81.5
Next best: take d20 with your d20, chance of winning the game: 80.75
There's only a 2% difference from worst to best among these three, so maybe it doesn't matter so much [though every percentage point matters], but I do think people tend to have a visceral preference for one type of move versus another in this sort of situation.
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