Craps puzzle

[MickeyHoldem]

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.

[VBCurtis]

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

[bobman0330]

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.

[RocketManJames]

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

[TomCollins]

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.

[TomCollins]

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.

[BruceZ]

[ 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.