Odds of all horn numbers before a 7
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)
