Probability

 ##################################################################
> # Probability of rolling a subset of numbers before a single number
> ##################################################################
>  start.time <- Sys.time()
>  options(scipen=999)
> 
> numbers = c(2,3,4,5,6,8,9,10,11,12,7)   # Last must occur only after all others in any order
> 
> in_36 = ifelse(numbers <= 7, numbers-1, 13-numbers)  # 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 0.1562679 secs
> p = 1-p
> p
[1] 0.005257704
> a=1/p
> a # 1 in 
[1] 190.1971
> a-1 # odds against
[1] 189.1971
> ##################################################################
> # Probability of rolling a subset of numbers before a single number
> ##################################################################
>  start.time <- Sys.time()
>  options(scipen=999)
> 
> numbers = c(2,3,4,5,6,4,5,6,8,6,8,9,8,9,10,10,11,12,7)   # Last must occur only after all others in any order
> 
> in_36 = c(1,2,2,2,2,1,2,2,2,1,2,2,1,2,2,1,2,1,6)  # 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 1.200368 secs
> p=1-p
> p
[1] 0.0001345821
> a=1/p
> a # 1 in 
[1] 7430.409
> a-1 # odds against
[1] 7429.409