Nutz Change Pair Bet Option
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3 members have voted
June 10th, 2018 at 7:10:19 AM
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Wizard wrote about the dice game Nutz in this post and provided complete analysis on this page.
You place a bet on Pair and a pair is set aside on the first roll. You are given the option to change your bet to any other result. What result should you choose?
You place a bet on Pair and a pair is set aside on the first roll. You are given the option to change your bet to any other result. What result should you choose?
“You don’t bring a bone saw to a negotiation.” - Robert Jordan, former U.S. ambassador to Saudi Arabia
June 10th, 2018 at 9:38:03 AM
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| Bet | Pays | Prob | Return |
|---|---|---|---|
| Nutz | 25 | 0.004630 | -0.879630 |
| Pair | 25 | 0.277778 | 6.222222 |
| Straight or No Hand | 9 | 0.000000 | -1.000000 |
| Quads | 5 | 0.069444 | -0.583333 |
| Trips | 5 | 0.277778 | 0.666667 |
| Two Pair | 3 | 0.277778 | 0.111111 |
| Full House | 2 | 0.092593 | -0.722222 |
The table above shows the probability of making each hand given that the first roll is a pair. So, the best thing to do is keep the bet on a pair, for an expected return of 622%. Seems high, as it seems I'm often stuck with a pair playing Yahtzee, but that is what my spreadsheet says.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
June 10th, 2018 at 12:51:11 PM
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| Bet | Occurance | Probability | Pays | Return |
|---|---|---|---|---|
| Pair | 109350 | 0.077160 | 25 | 1.006173 |
| Trips | 328050 | 0.231481 | 5 | 0.388889 |
| Two Pair | 371790 | 0.262346 | 3 | 0.049383 |
| Quads | 218700 | 0.154321 | 5 | -0.074074 |
| Full House | 353565 | 0.249486 | 2 | -0.251543 |
| Nutz | 35721 | 0.025206 | 25 | -0.344650 |
| Straight/No-Hand | 0 | 0.000000 | 9 | -1.000000 |
| Total | 1417176 | 1.000000 |
My conclusion agrees in general as far as what is +EV and what is not, and that keeping the pair bet is the best decision. However, I've got wildly different probabilities. That's strange, because my data as far as the overall game is concerned agrees with yours to six decimal places. Anyone want to take sides?
“You don’t bring a bone saw to a negotiation.” - Robert Jordan, former U.S. ambassador to Saudi Arabia
June 10th, 2018 at 12:55:58 PM
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Stab in the dark, re different figures, similar results :
Did both of you calculate that there are 2 more rolls to come until resolution, not just one?
Did both of you calculate that there are 2 more rolls to come until resolution, not just one?
If the House lost every hand, they wouldn't deal the game.
June 10th, 2018 at 1:02:53 PM
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Yes, I calculated the probabilities of results for the second roll and then the probabilities for the third roll on each of the second roll results.
“You don’t bring a bone saw to a negotiation.” - Robert Jordan, former U.S. ambassador to Saudi Arabia
June 10th, 2018 at 3:14:26 PM
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Quote: beachbumbabsDid both of you calculate that there are 2 more rolls to come until resolution, not just one?
That would seem to be my error. My table was for one more roll only.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
