Juergo70
Joined: Jan 7, 2022
• Posts: 5
January 7th, 2022 at 9:46:47 AM permalink
Hello all,

I am curious as to whether I am calculating the house edge on a craps strategy correctly.

The Wizard's house edge article says to divide the average return by the average bet. I calculated the percentage chance for each possible outcome - 40 in all. I multiplied each of those by the return for the outcome. I then added those all up. I then divided that sum by the average bet.

Is this correct? I got a very small number, so it seems wrong.

Any help would be appreciated.

Thank you!
Mission146
Joined: May 15, 2012
• Posts: 15308
January 7th, 2022 at 10:20:34 AM permalink
It would probably be best if you just state what, specifically, you were trying to figure out and then show us the work that you did on it.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Juergo70
Joined: Jan 7, 2022
• Posts: 5
Thanks for this post from:
January 7th, 2022 at 10:40:06 AM permalink
I am trying to calculate the house edge based on all the possible outcomes of a craps strategy.

Here's my work; sorry if the formatting is off. So, for example, in this strategy, 1.07% of the time, I'll lose \$27 on a \$90 bet, but .92% of the time, I'll win \$95 on a \$76 bet. If I am understanding the math, the sum of all outcomes is -\$1.92 with an average bet of \$72.30 giving the house an edge of 2.65%.

8.33% \$4.00 \$0.33 \$16
3.33% -\$50.00 -\$1.67 \$70
1.67% -\$16.00 -\$0.27 \$70
2.33% -\$15.00 -\$0.35 \$80
1.17% -\$21.00 -\$0.25 \$80
2.13% \$19.00 \$0.40 \$90
1.07% -\$27.00 -\$0.29 \$90
1.57% \$50.00 \$0.78 \$100
0.78% -\$36.00 -\$0.28 \$100
0.83% \$76.00 \$0.63 \$88
0.41% -\$22.00 -\$0.09 \$88
0.92% \$95.00 \$0.87 \$76
0.46% -\$15.00 -\$0.07 \$76
4.44% -\$50.00 -\$2.22 \$70
2.96% -\$16.00 -\$0.47 \$70
2.96% -\$15.00 -\$0.44 \$75
1.98% -\$16.00 -\$0.32 \$75
2.47% \$18.00 \$0.44 \$80
1.65% -\$18.00 -\$0.30 \$80
1.73% \$52.00 \$0.90 \$85
1.15% -\$19.00 -\$0.22 \$85
0.86% \$88.00 \$0.76 \$88
0.58% -\$20.00 -\$0.12 \$88
0.86% \$107.00 \$0.92 \$76
0.58% -\$13.00 -\$0.07 \$76
5.56% -\$48.00 -\$2.67 \$68
4.63% -\$16.00 -\$0.74 \$68
3.52% -\$13.00 -\$0.46 \$70
2.93% -\$13.00 -\$0.38 \$70
2.79% \$19.00 \$0.53 \$72
2.32% -\$13.00 -\$0.30 \$72
1.51% \$53.00 \$0.80 \$74
1.26% -\$11.00 -\$0.14 \$74
1.23% \$83.00 \$1.02 \$76
1.02% -\$13.00 -\$0.13 \$76
0.56% \$117.00 \$0.65 \$76
0.46% -\$13.00 -\$0.06 \$76
16.67% \$9.00 \$1.50 \$16
5.56% \$0.00 \$0.00 \$16
2.78% -\$6.00 -\$0.17 \$16

100.00% \$275.00 -\$1.92 \$72.30

House Edge -2.6507%
odiousgambit
Joined: Nov 9, 2009
• Posts: 8801
Thanks for this post from:
January 7th, 2022 at 10:45:31 AM permalink
Quote: Juergo70

Hello all,

I am curious as to whether I am calculating the house edge on a craps strategy correctly.

The Wizard's house edge article says to divide the average return by the average bet. I calculated the percentage chance for each possible outcome - 40 in all. I multiplied each of those by the return for the outcome. I then added those all up. I then divided that sum by the average bet.

Is this correct? I got a very small number, so it seems wrong.

Any help would be appreciated.

Thank you!

the expected value of a craps strategy involves adding up the expected value of each bet.

40 possible outcomes suggests 40 different bets, your strategy is unlikely to be that, so I think you have a mis-step right there

edit: I see up above your work. Yeah, you are going about this the wrong way. What is each bet? forget chances of outcomes for now
the next time Dame Fortune toys with your heart, your soul and your wallet, raise your glass and praise her thus: “Thanks for nothing, you cold-hearted, evil, damnable, nefarious, low-life, malicious monster from Hell!” She is, after all, stone deaf. ... Arnold Snyder
Mission146
Joined: May 15, 2012
• Posts: 15308
January 7th, 2022 at 10:49:56 AM permalink
Quote: Juergo70

I am trying to calculate the house edge based on all the possible outcomes of a craps strategy.

Here's my work; sorry if the formatting is off. So, for example, in this strategy, 1.07% of the time, I'll lose \$27 on a \$90 bet, but .92% of the time, I'll win \$95 on a \$76 bet. If I am understanding the math, the sum of all outcomes is -\$1.92 with an average bet of \$72.30 giving the house an edge of 2.65%.

8.33% \$4.00 \$0.33 \$16
3.33% -\$50.00 -\$1.67 \$70
1.67% -\$16.00 -\$0.27 \$70
2.33% -\$15.00 -\$0.35 \$80
1.17% -\$21.00 -\$0.25 \$80
2.13% \$19.00 \$0.40 \$90
1.07% -\$27.00 -\$0.29 \$90
1.57% \$50.00 \$0.78 \$100
0.78% -\$36.00 -\$0.28 \$100
0.83% \$76.00 \$0.63 \$88
0.41% -\$22.00 -\$0.09 \$88
0.92% \$95.00 \$0.87 \$76
0.46% -\$15.00 -\$0.07 \$76
4.44% -\$50.00 -\$2.22 \$70
2.96% -\$16.00 -\$0.47 \$70
2.96% -\$15.00 -\$0.44 \$75
1.98% -\$16.00 -\$0.32 \$75
2.47% \$18.00 \$0.44 \$80
1.65% -\$18.00 -\$0.30 \$80
1.73% \$52.00 \$0.90 \$85
1.15% -\$19.00 -\$0.22 \$85
0.86% \$88.00 \$0.76 \$88
0.58% -\$20.00 -\$0.12 \$88
0.86% \$107.00 \$0.92 \$76
0.58% -\$13.00 -\$0.07 \$76
5.56% -\$48.00 -\$2.67 \$68
4.63% -\$16.00 -\$0.74 \$68
3.52% -\$13.00 -\$0.46 \$70
2.93% -\$13.00 -\$0.38 \$70
2.79% \$19.00 \$0.53 \$72
2.32% -\$13.00 -\$0.30 \$72
1.51% \$53.00 \$0.80 \$74
1.26% -\$11.00 -\$0.14 \$74
1.23% \$83.00 \$1.02 \$76
1.02% -\$13.00 -\$0.13 \$76
0.56% \$117.00 \$0.65 \$76
0.46% -\$13.00 -\$0.06 \$76
16.67% \$9.00 \$1.50 \$16
5.56% \$0.00 \$0.00 \$16
2.78% -\$6.00 -\$0.17 \$16

100.00% \$275.00 -\$1.92 \$72.30

House Edge -2.6507%

I agree that is the percentage that you would get from all of the outcomes that you said. I guess what I am asking is, "What is the strategy?"

The average House Edge (assuming different bets are being made) is going to just be a function of your average bet on each proposition and the House Edge of the individual propositions being bet on.

I guess the problem from the numbers you have posted is that I don't even know what it is you're solving for. What is the strategy?
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Juergo70
Joined: Jan 7, 2022
• Posts: 5
Thanks for this post from:
January 7th, 2022 at 11:38:46 AM permalink
\$10 on Don't Pass; \$5 Any Seven; \$1 on Eleven. That's the \$16 you see at the top and bottom. Once the point is established, I do \$52/\$54 across. Then, as the place bets hit, I regress the place bets and use those and the winnings for odds. It's point dependent, such that the 4/10 is different from the 5/9 and the 6/8. That's why there are so possible outcomes and so many bets.

So, for example, in a perfect world:

Point is 4. Next roll is 6; win \$14. I take down the \$10 from the 10 and put \$20 up in odds. Next roll is 8; win \$14. I take down \$5 from the 5 and the 9 and put up \$20 in odds. Next roll is 8; win \$14. I take down \$5 from the 5 and 9 and put of \$20 in odds. Next roll is 6; win \$14. I take down \$6 from the 6 and 8. Next roll is 8; win \$7. Take down \$6 from 6 and 8. Next roll 7; win \$97.

There are 40 possible outcomes above. (There are actually more, but I used averages because sometimes there would be \$5 on one number and \$10 or \$12 on another, and the spreadsheet got real messy). Each shows the percentage of that result, the result, the return, and the bet at the time of the outcome. If my math is correct, then the overall house edge for this strategy across all the possible outcomes is 2.65%.
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 5360
Thanks for this post from:
January 7th, 2022 at 11:44:12 AM permalink
Quote: Juergo70

Hello all,

I am curious as to whether I am calculating the house edge on a craps strategy correctly.

The Wizard's house edge article says to divide the average return by the average bet. I calculated the percentage chance for each possible outcome - 40 in all. I multiplied each of those by the return for the outcome. I then added those all up. I then divided that sum by the average bet.

Is this correct? I got a very small number, so it seems wrong.

Is the "very small number" 2.6507% That's actually a relatively big number for craps. The house edge for a Pass bet is 1.414%.

It depends on what you mean by "divide by the average bet."
First, multiply the percentage chance of each possible (bet amount, result amount) pair by the result amount, and add those up.
Then, multiply the percentage chance of each possible (bet amount, result amount) pair by the bet amount, and add those up.
Divide the first by the second, and multiply by 100%.
Juergo70
Joined: Jan 7, 2022
• Posts: 5
Thanks for this post from:
January 7th, 2022 at 12:10:51 PM permalink
ThatDonGuy,

Ok. So, using my numbers above . . .

If there is a 0.86% chance of winning \$107 on a \$76 bet, you're saying that I need to (A) multiply the chance and the result (.0086*107 = .92) and (B) multiple the chance and the bet (.0086*76 = .6536)? Then do this for all possible outcomes. Add up all the numbers in A and add up all the numbers in B. Divide the sum A by the sum B and multiply 100?
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 5360
Thanks for this post from:
January 7th, 2022 at 12:21:03 PM permalink
Quote: Juergo70

ThatDonGuy,

Ok. So, using my numbers above . . .

If there is a 0.86% chance of winning \$107 on a \$76 bet, you're saying that I need to (A) multiply the chance and the result (.0086*107 = .92) and (B) multiple the chance and the bet (.0086*76 = .6536)? Then do this for all possible outcomes. Add up all the numbers in A and add up all the numbers in B. Divide the sum A by the sum B and multiply 100?

Yes.
Juergo70
Joined: Jan 7, 2022