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**14 members have voted**

The question for the poll is would you bet the Hot Hand bets if playing craps anyway?

From the picture, shouldn't the "Sizzling Six" be 4,5,6,8,9,10, and the "Flaming Four" be 2,3,11,12?

Quote:tringlomaneFrom the picture, shouldn't the "Sizzling Six" be 4,5,6,8,9,10, and the "Flaming Four" be 2,3,11,12?

D'oh! You're right. Just a labeling mistake, the math should be correct.

According to your math, it only pays 80:1.Quote:The object of the Hot Hand bet is to roll a 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12 before a total of seven. If this is accomplished, then winning bets shall pay 110 to 1.

That should be 9 out of 10...Quote:If 10 out of 11 of these totals are achieved before a seven, then winning bets shall pay 20 to 1.

It seems odd that what appears to be the feature bet doesn’t have the biggest payout. Having a 5 out of 6 as part of the Sizzling Six would fix that. It would also allow easier manipulation of the house edge.

Also, paying only 6:1 for the Flaming Four seems lame by comparison. Were it not for your math, I’d suspect an error with that and therefore question all these bets.

Quote:DJTeddyBearAlso, paying only 6:1 for the Flaming Four seems lame by comparison. Were it not for your math, I’d suspect an error with that and therefore question all these bets.

Thanks for your corrections. The math remains the same.

As to Flaming Four, if it paid 7 to 1, then the player would have a 5.4% advantage.

Quote:DJTeddyBear

Also, paying only 6:1 for the Flaming Four seems lame by comparison. Were it not for your math, I’d suspect an error with that and therefore question all these bets.

Me too. I don t expect anyone to play the "Flaming Four".

what are the rules? your success probabilities look way off, I feel you are using some rules like a comeout 7 the bet does not lose?Quote:WizardThanks for your corrections. The math remains the same.

As to Flaming Four, if it paid 7 to 1, then the player would have a 5.4% advantage.

I looked at some BruceZ R code he did for these type of problems

and here is what my simulations come close to (in Wincraps - done some time ago)

As to Flaming Four

##################################################################

> # Probability of rolling a subset of numbers before a single number

> ##################################################################

> start_time <- Sys.time()

> options(scipen=999)

>

> numbers = c(2,3,11,12,7) # Last must occur only after all others in any order

>

> in_36 = c(1,2,2,1,6) # Ways to make each number

> i = length(in_36)

> p = 0

> for (j in 1:(i-1)) { # Last number before j numbers

+ terms = combn(in_36[1:(i-1)],j) # Matrix w/combos of j numbers in C(i-1,j) columns

+ for (k in 1:ncol(terms)) { # Sum each column, compute and add probabilities

+ p = p + (-1)^(j+1) * in_36/(in_36 + sum(terms[1:j,k]))

+ }

+ }

> end_time <- Sys.time()

> time <- end_time - start_time

> time

Time difference of 0.28127 secs

> p=1-p

> p

[1] 0.01147186

back to the math

what am I overlooking?

0.01147186 is far from 0.131083

as the crow flies, naturally

for the box numbers I also got in Excel

0.062168159

just listing all the permutations

far from your 0.007213

fwiw,

I do like the bets, as they are more directly related to the game layout.

Box numbers and Horn numbers

simple

I just went to the casino online and found a rack card for this

"OVERVIEW

Hot Hand Dice is a series of side wages offered exclusively

at JACK casinos that are played in conjunction with any

standard craps game. All side wagers can be placed with

the selection of a new shooter or after the shooter rolls any

7. Available side wagers include the Sizzling 6, Flaming 4

and the Hot Hand wagers.

SIZZLING 6

Side wager pays 12 to 1 if the shooter rolls a 4, 5, 6, 8, 9 or

10, in any order, before rolling a 7, and loses otherwise.

FLAMING 4

Side wager pays 70 to 1 if the shooter rolls a 2, 3, 11 and 12,

in any order, before rolling a 7, and loses otherwise.

THE HOT HAND

Side wager pays 80 to 1 if the shooter rolls all ten possible

non-seven values before rolling a 7, pays 20 to 1 if the

shooter rolls any nine of the ten possible non-seven values

before rolling a 7, and loses otherwise.

* All Hot Hand Dice wagers will be settled immediately

following any roll of 7."

Flaming Four

Numbers | Probability | Pays | Return |
---|---|---|---|

0 | 0.50000000000 | -1 | -0.5 |

1 | 0.29090909091 | -1 | -0.2909090909 |

2 | 0.14393939394 | -1 | -0.1439393939 |

3 | 0.05367965368 | -1 | -0.05367965368 |

4 | 0.01147186147 | 70 | 0.803030303 |

Total | 1.00000000000 | -0.1854978355 |

Sizzling Six

Numbers | Probability | Pays | Return |
---|---|---|---|

0 | 0.20000000000 | -1 | -0.2 |

1 | 0.18598290598 | -1 | -0.185982906 |

2 | 0.17005723745 | -1 | -0.1700572374 |

3 | 0.15153125766 | -1 | -0.1515312577 |

4 | 0.12924473150 | -1 | -0.1292447315 |

5 | 0.10101570854 | -1 | -0.1010157085 |

6 | 0.06216815886 | 12 | 0.7460179064 |

Total | 1.00000000000 | -0.1918139348 |

Hot Hand

Numbers | Probability | Pays | Return |
---|---|---|---|

0 | 0.16666666667 | -1 | -0.1666666667 |

1 | 0.15486479049 | -1 | -0.1548647905 |

2 | 0.14210640274 | -1 | -0.1421064027 |

3 | 0.12823774477 | -1 | -0.1282377448 |

4 | 0.11308227693 | -1 | -0.1130822769 |

5 | 0.09645525120 | -1 | -0.0964552512 |

6 | 0.07821985752 | -1 | -0.07821985752 |

7 | 0.05845341082 | -1 | -0.05845341082 |

8 | 0.03789744720 | -1 | -0.0378974472 |

9 | 0.01875844756 | 20 | 0.3751689512 |

10 | 0.00525770410 | 80 | 0.4206163277 |

Total | 1.00000000000 | -0.1801985695 |