How much of a change do i need?

[OrangeHeat]

As this is general probability....

How much dwould these "proposed dice setters" on the history channel need to alter the probability of rolling a seven to make the pass line bet profitable???

for example chances of rolling a seven are 5:1 or 1 seven for every 6 rolls.

what does this need to change to 6:1, 7:1?

Please ignore odds behind the line. I think the house edge starts at 1.414% with just the pass line bet.

The math would be helpful too,

Thanks,

Orange

[AaronBrown]

In fair craps, you have 1/9 chance of losing on the come out roll, and 2/9 chance of winning. The other 6/9 of the time you make a point, and win 0.40606 of those. Multiply it out and you get a 0.492929 chance of winning, or a house edge of 1.4141% as you say.

Let's say that X fraction of the time I get a 7 on the come out roll and 1-X of the time I play fair craps. That is, I only affect the chance of a 7 on the come out roll and, if my manipulation doesn't work, I just get a fair game. Then we need to solve:

X + (1 - X)*0.492929 = 0.5

which we can reduce to:

0.507071*X = 0.007071

or

X = 0.007071/0.507071

or

X = 0.013944.

So if you can force a 7 1.3944% of the time, and a fair roll the rest of the time, in other words, get 7 a total of 1/6 + 1.3944% = 18.0611% of the time; you eliminate the house edge.

[OrangeHeat]

Thanks!

Orange