December 16th, 2018 at 7:46:06 AM
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I want to roll all of the four hardest numbers (2,3,11,and 12) before I throw a seven. Repeats are allowed and other numbers don't matter. What are the odds of this event happening?

December 16th, 2018 at 9:01:50 AM
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this is only when using standard dice (2d6)Quote:vince711I want to roll all of the four hardest numbers (2,3,11,and 12) before I throw a seven. What are the odds of this event happening?

using R code from this thread (code original by BruceZ)

https://wizardofvegas.com/forum/gambling/craps/19239-craps-side-bets-odds-calculation/#post386972

# odds against

about 86.16981 to 1

about 1 chance in 87.16981

> p

[1] 0.01147186

> a=1/p

> a # 1 in

[1] 87.16981

> a-1 # odds against

[1] 86.16981

code

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

# 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

p=1-p

p

a=1/p

a # 1 in

a-1 # odds against

that should lead to

"Why do you want to roll all of the four hardest numbers (2,3,11,and 12) before you throw a seven?"

there are (on any one roll) 6 ways to roll a Seven and 6 ways to roll any Horn

winsome johnny (not Win some johnny)

December 16th, 2018 at 9:13:13 AM
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Thank you. The topic came up in a discussion a few of us were having with the "all tall - all small" bonus bets taking over many layouts. We were wondering what the odds were for the four toughest pieces.

December 16th, 2018 at 10:03:02 AM
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that is what I figured.Quote:vince711Thank you. The topic came up in a discussion a few of us were having with the "all tall - all small" bonus bets taking over many layouts. We were wondering what the odds were for the four toughest pieces.

even my small town in Nevada has only 1 craps table, offers those wagers. Not hit that often when I do watch.

the R code can be used for any subset before a 7.

I think there is another thread on that.

the all small and all tall way easier (even though there are more numbers to collect)

> p=1-p

> p

[1] 0.02635391

> a=1/p

> a # 1 in

[1] 37.94503

> a-1 # odds against

[1] 36.94503

the all or nothing at all

harder (more numbers to make)

> p

[1] 0.005257704

> a=1/p

> a # 1 in

[1] 190.1971

> a-1 # odds against

[1] 189.1971

what is way easier (and not offered as a bet)

are all the box numbers before the 7

> p

[1] 0.06216816

> a=1/p

> a # 1 in

[1] 16.0854

> a-1 # odds against

[1] 15.0854

winsome johnny (not Win some johnny)

December 16th, 2018 at 10:17:39 AM
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Since we are on the topic, how about the odds of throwing all 6 sets of doubles before a 7 (1-1, 2-2, 3-3, 4-4, 5-5 and 6-6) ? Anything other than a 7 doesn't matter. Another "craps table conversation" (not to be confused with hard/soft concept). Obviously by the question, me and my buddies may spend too much time at the table.

December 16th, 2018 at 10:32:45 AM
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923 to 1 against (easier that that old Fire Bet)Quote:vince711Since we are on the topic, how about the odds of throwing all 6 sets of doubles before a 7 (1-1, 2-2, 3-3, 4-4, 5-5 and 6-6) ?

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

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

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

> start_time <- Sys.time()

> options(scipen=999)

>

> numbers = c(2,4,6,8,10,12,7) # Last must occur only after all others in any order. all doubles

>

> in_36 = c(1,1,1,1,1,1,6) # 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 0.1718011 secs

> p=1-p

> p

[1] 0.001082251

> a=1/p

> a # 1 in

[1] 924

> a-1 # odds against

[1] 923

>

LOL. never too much timeQuote:vince711Obviously by the question, me and my buddies may spend too much time at the table.

added

I think that these other type of bets would not be offered

as they would be a part of a bet already on the layout.

It could easily be done on a craps machine, but have yet to see the Bonus Craps bets there.

for fun - some data

sorted from highest odds against to lowest

name | numbers (before a 7) | prob | 1 in | odds against to 1 |
---|---|---|---|---|

Hardways | 4,6,8,10 (before a loss) | 0.000136705 | 7,315 | 7,314 |

Doubles | 2,4,6,8,10,12 | 0.001082251 | 924 | 923 |

all or nothing at all | 2,3,4,5,6,8,9,10,11,12 | 0.005257704 | 190.1971 | 189.1971 |

Hardways | 6&8 (before a loss) | 0.008333333 | 120 | 119 |

Hardways | 4&6 mix (before a loss) | 0.01098901 | 91 | 90 |

Horn | 2,3,11,12 | 0.01147186 | 87.16981 | 86.16981 |

Hardways | 4&10 (before a loss) | 0.01515152 | 66 | 65 |

all small | 2,3,4,5,6 | 0.02635391 | 37.94503 | 36.94503 |

all tall | 8,9,10,11,12 | 0.02635391 | 37.94503 | 36.94503 |

Box Numbers | 4,5,6,8,9,10 | 0.06216816 | 16.0854 | 15.0854 |

Outside | 4,5,9,10 | 0.08550959 | 11.69459 | 10.69459 |

Inside | 5,6,8,9 | 0.1310834 | 7.628732 | 6.628732 |

6&8 | 6,8 | 0.2840909 | 3.52 | 2.52 |

Last edited by: 7craps on Dec 16, 2018

winsome johnny (not Win some johnny)