I Math question regarding the game of craps

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1. Mar 7, 2016

eiyaz

Not sure if anyone plays craps here, but I think one of the probabilities is wrong.The C and E bet which is a single roll on craps (2,3,12, four total possible combinations for 2 dice which has 36 total possible combinations) or on 11 (yo) which has two combinations for a total of six combinations. Your bet is split between the two bets so this bet must an even number, split between craps and 11.

If 11 rolls you have 15:1 payout on half your bet and the other on craps lose. If craps (2,3,12) is rolled you have a 7:1 payout on half your money and lose the half on 11. For example if you bet $2 on the C and E the dealer will put$1 on each. If craps is rolled you get $7 -$1 you lose on 11 so total profit is $6, you can take the$1 on craps back if you wish. If an eleven is rolled you get 15:1 on your $1 not$2, because the bet is split so you would profit $14 dollars$15 - $1 you had on C (craps). Because you lose half your money when this bet wins and lose everything when a number other than craps or 11 is rolled, shouldn't the house edge be better than 11.11% (as in worse for the player higher house edge than 11.11%)? If you bet on the 11 alone you get 15:1 payout when the true odds are 17:1 for an 11.11% house edge. How can this be the same if you are making a bet on the C and E where you lose half your bet even if you win? Are the odds on Wikipedia right? Last edited: Mar 7, 2016 2. Mar 7, 2016 Buzz Bloom Hi eiyaz: CORRECTION My expectation calculation is that the house averages taking 11.111. . . cents out of every dollar bet. Wikipedia says that the odds given is 7:1 odds for the 11 bet, and 3:1 odds on the craps bet. If 11, better wins 3. 3 x 4 rolls = 12 If craps, better wins 7. 7 x 2 rolls = 14 If other, better loses 1. -1 x 30 rolls = -30 Net = -4 4/36 = 1/9 = 0.111... I am not sure what you mean by "odds" here. Wikipedia says "True Odds = 5:1". I assume that this means that the better wins something on 6 rolls and loses 1 on 30 rolls. Wikipedia says "House Edge = 11.11%". Regards, Buzz Last edited: Mar 7, 2016 3. Mar 7, 2016 eiyaz Thanks, just to confirm Wikipedia's article on Craps (https://en.wikipedia.org/wiki/Craps#Bet_odds_and_summary) says 11.11% this is wrong correct this actual number should be 13.8%? Wait you have six combinations (1-1, 1-2, 2-1, 6-6, 5-6, 6-5,) so its 6/36 I think, but the thing is you lose half your bet so craps is (1-1, 1-2, 2-1, 6-6) and get 7:1 payout on half your money so if you bet$2 you win 7:1 on $1 and lose the$1 on 11 (yo) so you get $6 net profit ($7 - $1 on the 11) you can still take the$1 on craps back for a total revenue of $7. If 11 (5-6, 6-5) rolls you get 15:1 on$1 and lose the $1 on craps (1-1, 1-2, 2-1, 6-6) so net profit is$14 plus you can take the $1 on 11 back for a total revenue of$15. If any other number besides craps or 11 comes you lose your whole bet on (both bets), this is a single roll bet. Is the 11.11% correct? I was thinking it should be between 11.11% and 13.88% because you still lose half your bet when you win.

Last edited: Mar 7, 2016
4. Mar 7, 2016

eiyaz

That's true odds and its 17:1 not 16:1 and 8:1.
True Odds for Craps (1-1, 1-2, 2-1, 6-6) is 8:1 payout is only 7:1
True Odds for 11 (5-6, 6-5) is 17:1 payout is only 15:1

However, if you bet C and E you are betting both, so you are only paid 15:1 or 7:1 (depending on 11 or craps) on half your bet. If you bet on 11 alone (not C and E) you get 15:1 payout but you also get your whole investment back so the house edge is 11.11%, a bet on the C and E has more possibilities yes, but is the odds the same 11.11% when you only get half your original bet back?

5. Mar 7, 2016

6. Mar 7, 2016

Buzz Bloom

Hi @eiyaz:

Sorry about my mistakes in earlier versions of my previous post. Please look at the corrected version.

Regards,
Buzz

7. Mar 7, 2016

eiyaz

Does that include the fact you lose half your bet on C or E when you win? I was under the impression that the calculations out there did not include this fact, I am not sure though

Last edited: Mar 7, 2016
8. Mar 7, 2016

Buzz Bloom

Hi @eiyaz:

No. The odds given
"Wikipedia says that the odds given is 7:1 odds for the 11 bet, and 3:1 odds on the craps bet."
assumes a single bet on the CE combination. This would actually correspond to making a $0.50 bet on each of (a) the 11, and (b) craps. The (a) bet would pay 16:1 and the (b) bet 8:1. The$0.50 bet on 11 would return a gain of $8 minus the dollar bet = 7:1. The$0.50 bet on craps would return a gain of $4 minus the dollar bet = 3:1. Regards, Buzz 9. Mar 7, 2016 eiyaz That is a calculation for the total bet. If you were to bet$2 and you hit craps you get $6 in net profit plus half your original bet back for 3:1 on$2 and a total revenue of $7. If you were to bet$2 and 11 (yo) came you would get 7:1 on $2 for$14 of net profit but you would only get back $1 for 11 not$2 for a total revenue of $15 since the craps (C) bet lost. Wikipedia did not mention you do not get back your whole bet back just half. 10. Mar 7, 2016 Buzz Bloom Hi eiyaz: I am not sure what you mean by "the total bet". (1) Bet$0.50 on craps and $0.50 on 11. (2) Bet$1 on the EC combination.

Please choose one of the above.

Regards,
Buzz