#1
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Craps puzzle
You have the ability to make loaded dice.
You can create a die that has a 1/5 chance of falling on one number. The side opposite this number will have 2/15 chance of coming up and the other 4 sides remain 1/6. If you could introduce 2 of these into a craps game, what numbers would you "load" on each die, and what bet would you play to create the greatest EV for yourself. |
#2
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Re: Craps puzzle
How about 4 on both? This makes the P(8) highest, while also decreasing p(7), since 4 is weighted higher while 3 is weighted lower on each die, so when one die hits 4, chance of 7 is reduced even further.
I did no calculations-- figured posting would prompt me to compute a little. I can see 2/2 (or 5/5) as also profitable, but then you'd win more perhaps by placing the 4 (10), instead of just pass line. I'll take a stab at seeing if the weighted dice make up for house edge on placing the 4... seems a harder problem to calculate if placing the 8 instead of pass line is more profitable in first case. -Curtis |
#3
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Re: Craps puzzle
Loading 5-5 and betting the pass line seems like a good play. Any equal doubles weighting has the same effect on P(rolling a 7). 5-5 increases the chances of rolling an 11 without increasing the chance of a 12 and while decreasing 3s. More calculations later.
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#4
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Re: Craps puzzle
Here's a first try for me:
Load both dies so that 1 hits most often. Bet the snake eyes paying 30 to 1. You should hit it 1/25, so this gives you 24 cents per dollar wagered long term. -RMJ |
#5
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Re: Craps puzzle
I'm gonna simplify it and say only betting on the pass line to find the biggest edge. Someone else take the don't pass, or take other bets. Something tells me a hardway bet is gonna be the best bet.
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#6
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Re: Craps puzzle
Pass and Don't Pass:
1 1 0.482735 0.508376 1 2 0.482192 0.5066971 1 3 0.487769 0.5011201 1 4 0.487708 0.5011807 1 5 0.493441 0.4954478 1 6 0.493045 0.493217 2 2 0.483737 0.5023737 2 3 0.487759 0.4983517 2 4 0.487599 0.4985119 2 5 0.491823 0.4942876 2 6 0.493441 0.4898922 3 3 0.494858 0.4912526 3 4 0.491494 0.4946168 3 5 0.49871 0.4874008 3 6 0.498819 0.484514 4 4 0.494858 0.4912526 4 5 0.498871 0.4872406 4 6 0.49888 0.484434 5 5 0.50596 0.4801515 5 6 0.504414 0.4789193 6 6 0.504957 0.4750427 So the edge is 1.19% for 5-5 weighted Pass. And the edge is .25% for 1-1 weighted Don't Pass. |
#7
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Re: Craps puzzle
[ QUOTE ]
Here's a first try for me: Load both dies so that 1 hits most often. Bet the snake eyes paying 30 to 1. You should hit it 1/25, so this gives you 24 cents per dollar wagered long term. -RMJ [/ QUOTE ] Good, but nosed out by the hardway 3:3 or 4:4 paying 9:1 with proper odds of 6.89-to-1, and pays 26.8 cents on the dollar. Yours requires slightly fewer rolls to pay off on average (25 vs. 29), which makes up for the small difference in EV. |
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