Gaffed Die

Assuming that:
(1) one die was “gaffed” in a private craps game, which resulted in a single side of that die appearing 10% less often
(2) the second die is fair
(3) 2/12 field bets pay 2x/3x

How do I calculate the EV and HE on every table bet based on “gaffed” sides 1-6?

I don't know how to answer most of it, but here is a list of %'s (to try and help you out) for: "when both dice are fair" and "if one die is fair and one isn't",

Note: the chance figures below are based on, if the 1 had a 15% chance of being rolled on the "gaffed" die, all other numbers are 17% each on the "gaffed" die, and fair odds on the other die.

"One gaffed and one fair":
2: 1/40
3: 4/75
4: ~4/49
5: ~10/91
6: ~4/29
7: 1/6
8: ~20/141
9: ~10/88
10: ~4/47
11: ~5/88
12: ~3/106

Both dice fair:
2 or 12 : 1/36 each
3 or 11: 1/18 each
4 or 10: 1/12 each
5 or 9: 1/9 each
6 or 8: 5/36 each
7: 1/6

Quote: Polo

Assuming that:
(1) one die was “gaffed” in a private craps game, which resulted in a single side of that die appearing 10% less often
(2) the second die is fair
(3) 2/12 field bets pay 2x/3x

How do I calculate the EV and HE on every table bet based on “gaffed” sides 1-6?
link to original post

Assuming the gaffed die is not mercury filled or adjustable, don't we need to know which face it favours?

Kudos to the trenchant query by Once Dear. Furthermore, why does anyone choose the onanism of deeply analyzing strictly hypothetical fantasies?

Pure math for its own sake is an entirely separate matter.

Quote: OnceDear

Quote: Polo

....How do I calculate the EV and HE on every table bet based on “gaffed” sides 1-6?
link to original post

Assuming the gaffed die is not mercury filled or adjustable, don't we need to know which face it favours?

I think that was part of the original question...a solution where each side 1-6 is gaffed.

Ex. “gaffed” die A reduces the appearance of the number 1 from 1/6 to 3/20 (calculate EV and HE)
“gaffed” die B reduces the appearance of the number 2 from 1/6 to 3/20 (calculate EV and HE)

…and so on.

Quote: pwcrabb

... why does anyone choose the onanism of deeply analyzing strictly hypothetical fantasies?

Pure math for its own sake is an entirely separate matter.
link to original post

Although we have something of an informal policy about not doing homework, you answered your own question. It's fun.


With normal dice, the entry in all 36 cells of a spreadsheet is = (1/6) * (1/6)

When the gaff results in one side of that die appearing 10% less, the formula for that row becomes = ((1/6)*.9) * (1/6)

The key is, you gotta give one fifth of that 10% to the other 5 sides.

Therefore, the formula for the other five rows becomes = ((1/6)+(1/6)*.1*(1/5)) * (1/6)

Of course now that you know how the formula works, you can gaff the other die, or gaff them different amounts.

Quote: OnceDear

...don't we need to know which face it favours?
link to original post

Yup. And once we know that, we will be able to determine the third part of the original question: The field bet payout totals.

As long as the total of the 36 cells adds up to 1, your formulas are good.

Quote: DJTeddyBear

The key is, you gotta give one fifth of that 10% to the other 5 sides.

Therefore, the formula for the other five rows becomes = ((1/6)+(1/6)*.1*(1/5)) * (1/6)

Of course now that you know how the formula works, you can gaff the other die, or gaff them different amounts.

Quote: OnceDear

...don't we need to know which face it favours?
link to original post

Yup. And once we know that, we will be able to determine the third part of the original question: The field bet payout totals.

As long as the total of the 36 cells adds up to 1, your formulas are good.
link to original post

If it is a physically gaffed die... Is there any other sort? Then is it not possible that the face opposite to the one favoured would bear all, or most of the cost of the gaffing. So would we adjust every other side, or would we just strongly adjust the ONE un-favoured face?

Quote: OnceDear

Quote: DJTeddyBear

The key is, you gotta give one fifth of that 10% to the other 5 sides.

Therefore, the formula for the other five rows becomes = ((1/6)+(1/6)*.1*(1/5)) * (1/6)

Of course now that you know how the formula works, you can gaff the other die, or gaff them different amounts.

Quote: OnceDear

...don't we need to know which face it favours?
link to original post

Yup. And once we know that, we will be able to determine the third part of the original question: The field bet payout totals.

As long as the total of the 36 cells adds up to 1, your formulas are good.
link to original post

If it is a physically gaffed die... Is there any other sort? Then is it not possible that the face opposite to the one favoured would bear all, or most of the cost of the gaffing. So would we adjust every other side, or would we just strongly adjust the ONE un-favoured face?
link to original post

I would interpret the OP as side A is 90/600, and all other sides are 102/600. The OP does not ask HOW one could construct a die that behaves that way, just states that it does. An additional clarifying statement such as ‘all other sides are rolled at a 2% increased frequency’ would likely satisfy your question.

Correct, all other sides will appear at a 2% increased frequency. Thank you for clarifying, SOOPOO.

Quote: OnceDear

If it is a physically gaffed die... Is there any other sort? Then is it not possible that the face opposite to the one favoured would bear all, or most of the cost of the gaffing. So would we adjust every other side, or would we just strongly adjust the ONE un-favoured face?
link to original post

Not necessarily.

Just like your question of WHICH face is gaffed, we need to know HOW it was gaffed before you can make the assumption that the entire reduction in odds of one face is added to odds of the face on the other side.

Since the OP didn't say it, I did the math to attribute it equally.

Quote: SOOPOO

I would interpret the OP as side A is 90/600, and all other sides are 102/600. The OP does not ask HOW one could construct a die that behaves that way, just states that it does. An additional clarifying statement such as ‘all other sides are rolled at a 2% increased frequency’ would likely satisfy your question.
link to original post

Damn.

90/600 and five at 102/600 is much simpler. And easier to understand. Even .9 / 6 and 1.02 / 6 is simpler.

And I HATE fractions.

Apparently this site sells them. $50. They look legit.

https://store.theory11.com/products/gaff-dice-jason-england

On edit…ooops, appears the “gaff” is merely same pips.