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BleedingChipsSlowly
BleedingChipsSlowly
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June 10th, 2018 at 7:10:19 AM permalink
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 don’t bring a bone saw to a negotiation.” - Robert Jordan, former U.S. ambassador to Saudi Arabia
Wizard
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Wizard
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June 10th, 2018 at 9:38:03 AM permalink

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)
BleedingChipsSlowly
BleedingChipsSlowly
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June 10th, 2018 at 12:51:11 PM permalink

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
beachbumbabs
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June 10th, 2018 at 12:55:58 PM permalink
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?
If the House lost every hand, they wouldn't deal the game.
BleedingChipsSlowly
BleedingChipsSlowly
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June 10th, 2018 at 1:02:53 PM permalink
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
Wizard
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June 10th, 2018 at 3:14:26 PM permalink
Quote: beachbumbabs

Did 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)
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