Calculating House Edge

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!

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.

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%

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!
link to original post

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

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%
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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?

$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%.

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%.

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?

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?
link to original post

Yes.

Thank you so much! I really appreciate your help.

I see now that that strategy sucks, and will not be used. Which was the goal of the exercise.

All the best,

J

all strategy that involves any combination of negative expectation bets will result in an overall negative expectation. You don't need to crunch the numbers.