Modified crapless craps math

Hi Wizard , is this math correct ?

The house advantage for the pass line bet in No-Crap Craps is 1.414 percent, exactly as it is in standard craps. This is easy to see. The only differences between the pass line bet in No-Crap Craps and the pass line bet in standard craps occur when 2, 3, 11, or 12 is rolled on the come-out roll. These numbers contribute (−1)(4/36)+(1)(2/36)=−2/36 to the pass line bettor's expectation in standard craps. In No-Crap Craps these numbers contribute 2(3/36)((1)(3/(3+6))+(−1)(6/(3+6)))=−2/36, which is identical.

These are the rules of this modified Crapless craps game
There is a very interesting variation of crapless craps that allegedly has the same house edge as regular craps also allows DP and Don’t Come but the points of 2/3 and 11/12 are together …true odds on a 2/3 or a 11/12 is 2-1 same as a 4 or 10 ! ( 3 ways to make those as opposed to 6 for Big Red ) If u place the 2/3 or 11/12 same payouts as a 4 and 10

Quote: cptave

Hi Wizard , is this math correct ?

The house advantage for the pass line bet in No-Crap Craps is 1.414 percent, exactly as it is in standard craps. This is easy to see. The only differences between the pass line bet in No-Crap Craps and the pass line bet in standard craps occur when 2, 3, 11, or 12 is rolled on the come-out roll. These numbers contribute (−1)(4/36)+(1)(2/36)=−2/36 to the pass line bettor's expectation in standard craps. In No-Crap Craps these numbers contribute 2(3/36)((1)(3/(3+6))+(−1)(6/(3+6)))=−2/36, which is identical.

These are the rules of this modified Crapless craps game
There is a very interesting variation of crapless craps that allegedly has the same house edge as regular craps also allows DP and Don’t Come but the points of 2/3 and 11/12 are together …true odds on a 2/3 or a 11/12 is 2-1 same as a 4 or 10 ! ( 3 ways to make those as opposed to 6 for Big Red ) If u place the 2/3 or 11/12 same payouts as a 4 and 10

The first paragraph is not correct.

The 2, 3 and 12 turn from sure losers to probably losers (hard point to make).

11 turns from sure winner to probably loser.

-EV trade.

This is the math from a modified crapless craps game ( read my second paragraph)

in this modified crapless craps game a point of 2 and 3 can be made when EITHER a 2 or a 3 roll
( same with the 11 or 12) This makes those points only as hard as making a point of 4 or 10 and as there are 3 ways to make a 2 or 3 versus 6 ways to make a 7 those points will pay the true odds of 2-1 ( i don't need the Wizard to confirm that !)

i would like the Wizard to confirm that both regular craps and this modified Crapless craps have a 1.414% House Edge !

Quote: cptave

In No-Crap Craps these numbers contribute 2(3/36)((1)(3/(3+6))+(−1)(6/(3+6)))=−2/36, which is identical.

Where do you get 3 / (3 + 6) for making any of the points 2, 3, 11, or 12?

In No-Crap Craps, they contribute:
Point of 2 or 12: 2/36 x (1 x (1 / (1 + 6)) + (-1) x (6 / (1 + 6))) = 2/36 x (1/7 - 6/7) = -5/126
Point of 3 or 11: 4/36 x (1 x (2 / (2 + 6)) + (-1) x (6 / (2 + 6))) = 4/36 x (2/8 - 6/8) = -1/18 = -7/126
Total = -12/126 = -2/21

This is a modified crapless craps game ( no casino has it yet ) a point of 2 and 3 can be made when EITHER a 2 or a 3 roll
( same with the 11 or 12) This makes those points only as hard as making a point of 4 or 10 and as there are 3 ways to make a 2 or 3 versus 6 ways to make a 7 those points will pay the true odds of 2-1 ( i don't need the Wizard to confirm that !)

Quote: cptave

This is a modified crapless craps game ( no casino has it yet ) a point of 2 and 3 can be made when EITHER a 2 or a 3 roll
( same with the 11 or 12) This makes those points only as hard as making a point of 4 or 10 and as there are 3 ways to make a 2 or 3 versus 6 ways to make a 7 those points will pay the true odds of 2-1 ( i don't need the Wizard to confirm that !)

In that case, then yes, the house edge on Pass is the same.

What I, and presumably others, would like to know is, where do they actually play it this way?

It seems a neat idea and they might even be able to offer don't pass!

Essentially if you roll a 2 3 11 or 12, then in standard craps you have a 1/3 chance of winning (11 wins, 2 3 12 loses). In this game either (2 and 3) or (11 and 12) have a chance of being rerolled of 1/3. So if you roll a 2 3 11 or 12 you still have a 1/3 chance of winning.

Interestingly it also has the option of adding a place box of "2 or 3" and "11 or 12" (with hardway options as well) identical odds to those of 4 and 10.

Quote: ThatDonGuy

In that case, then yes, the house edge on Pass is the same.

What I, and presumably others, would like to know is, where do they actually play it this way?

do not think it has ever made it to the casino.

Was 'invented' by Stewart N. Ethier (the college math guy)
Patent No.: US 7,134,660 B2
Date of Patent: Nov. 14, 2006

That version has been discussed before.

the '2 or 3' bet and '11 or 12' bet was added at 2 to 1 odds payout.
nothing new and most love the 6 to 1 odds payoff of crapless craps. (my experience)
I set up and played that version on my laptop years ago
and was not impressed. It did not 'grab' me in any way.

it might grab others

as to the OP, math looks correct.
the math is also spelled out in the patent

Quote: 7craps

do not think it has ever made it to the casino.

Was 'invented' by Stewart N. Ethier (the college math guy)
Patent No.: US 7,134,660 B2
Date of Patent: Nov. 14, 2006

That version has been discussed before.

the '2 or 3' bet and '11 or 12' bet was added at 2 to 1 odds payout.
nothing new and most love the 6 to 1 odds payoff of crapless craps. (my experience)
I set up and played that version on my laptop years ago
and was not impressed. It did not 'grab' me in any way.

it might grab others

as to the OP, math looks correct.
the math is also spelled out in the patent

getting 6-1 with a 5% vig paid on win only is pretty sweet.