vince711
vince711
Joined: Dec 16, 2018
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December 16th, 2018 at 7:46:06 AM permalink
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?
7craps
7craps
Joined: Jan 23, 2010
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  • Posts: 1977
December 16th, 2018 at 9:01:50 AM permalink
Quote: vince711

I 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?

this is only when using standard dice (2d6)
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)
vince711
vince711
Joined: Dec 16, 2018
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December 16th, 2018 at 9:13:13 AM permalink
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.
7craps
7craps
Joined: Jan 23, 2010
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  • Posts: 1977
December 16th, 2018 at 10:03:02 AM permalink
Quote: vince711

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.

that is what I figured.
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)
vince711
vince711
Joined: Dec 16, 2018
  • Threads: 1
  • Posts: 3
December 16th, 2018 at 10:17:39 AM permalink
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.
7craps
7craps
Joined: Jan 23, 2010
  • Threads: 18
  • Posts: 1977
December 16th, 2018 at 10:32:45 AM permalink
Quote: vince711

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) ?

923 to 1 against (easier that that old Fire Bet)
> ##################################################################
> # 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
>

Quote: vince711

Obviously by the question, me and my buddies may spend too much time at the table.

LOL. never too much time

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
namenumbers (before a 7)prob1 inodds against to 1
Hardways4,6,8,10 (before a loss)0.0001367057,3157,314
Doubles2,4,6,8,10,120.001082251924923
all or nothing at all2,3,4,5,6,8,9,10,11,120.005257704190.1971189.1971
Hardways6&8 (before a loss)0.008333333120119
Hardways4&6 mix (before a loss)0.010989019190
Horn2,3,11,120.0114718687.1698186.16981
Hardways4&10 (before a loss)0.015151526665
all small2,3,4,5,60.0263539137.9450336.94503
all tall8,9,10,11,120.0263539137.9450336.94503
Box Numbers4,5,6,8,9,100.0621681616.085415.0854
Outside4,5,9,100.0855095911.6945910.69459
Inside5,6,8,90.13108347.6287326.628732
6&86,80.28409093.522.52
Last edited by: 7craps on Dec 16, 2018
winsome johnny (not Win some johnny)

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