Quote Originally Posted by Cacarulo View Post
Hi,

Still don't get the subgroup thing. For instance, if I wanted an insurance index for AAvA, I'll remove
three aces from the pack. If I wanted an index for A2vA, I'll remove two aces. What am I missing?

Sincerely,
Cac
Start with cards remaining and running count.

My view is that the number of cards removed in a subgroup is input directly. That number remains absolute. (Subgroup cards present is determined from subgroup cards removed.) The number of variable cards is (input cards remaining - subgroup cards present). Since subgroup cards present are a given, probability of subset is independent of subgroup input.

The maximum number of subgroups is 10. In that case removals of all ten ranks would be input to define 1 possible subset. If what is input is not possible the probability of the subset will turn out to be 0. This dovetails into just inputting a shoe composition from scratch. That is the extreme.

A subgroup must be defined from 1 or more ranks in a main group. HiLo has 3 main groups: {2,3,4,5,6}, {7,8,9}, {T,A}

I'm trying to come up with an obvious example using HiLo. I've added notes to each of 4 inputs of 26 cards remaining of a single deck to try to help explain a subgroup defined as {7,8,9}. Basically number of {7,8,9} is being independently input.

26 cards remain, Subgroup {7,8,9}
RC, subgroup cards, and specific removals are input
There are 4 inputs with resultant rank probs p[1] through p[10]
Code:
Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Decks: 1
Cards remaining: 26
Initial running count (full shoe): 0
Running count: 0
Specific removals (1 - 10): {0,0,0,0,0,0,0,0,0,0}
Subgroup removals: {7,8,9}12

Number of subsets for above conditions: 1 (Note: subset is 13{2,3,4,5,6}, 0{7,8,9}, 13{T,A})
Prob of running count 0 with above removals from 1 deck: 0.25895

p[1] 0.1  p[2] 0.1  p[3] 0.1  p[4] 0.1  p[5] 0.1
p[6] 0.1  p[7] 0  p[8] 0  p[9] 0  p[10] 0.4


Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Decks: 1
Cards remaining: 26
Initial running count (full shoe): 0
Running count: -1
Specific removals (1 - 10): {0,0,0,0,0,0,0,0,0,0}
Subgroup removals: {7,8,9}12

Number of subsets for above conditions: 0 (Note: subset is impossible - need odd num cards for RC=-1 and 0 {7,8,9})
Prob of running count -1 with above removals from 1 deck: 0.00000e+000

p[1] 0  p[2] 0  p[3] 0  p[4] 0  p[5] 0
p[6] 0  p[7] 0  p[8] 0  p[9] 0  p[10] 0


Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Decks: 1
Cards remaining: 26
Initial running count (full shoe): 0
Running count: 0
Specific removals (1 - 10): {0,0,0,0,0,0,0,0,0,0}
Subgroup removals: {7,8,9}6

Number of subsets for above conditions: 1 (Note: subset is 10{2,3,4,5,6}, 6{7,8,9}, 10{T,A})
Prob of running count 0 with above removals from 1 deck: 0.24763

p[1] 0.076923  p[2] 0.076923  p[3] 0.076923  p[4] 0.076923  p[5] 0.076923
p[6] 0.076923  p[7] 0.076923  p[8] 0.076923  p[9] 0.076923  p[10] 0.30769


Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Decks: 1
Cards remaining: 26
Initial running count (full shoe): 0
Running count: 0
Specific removals (1 - 10): {0,0,0,0,0,0,1,0,0,0}
Subgroup removals: {7,8,9}6 (Note: range of input here is 1-12, since a 7 was specifically removed)

Number of subsets for above conditions: 1
Prob of running count 0 with above removals from 1 deck: 0.24763

p[1] 0.076923  p[2] 0.076923  p[3] 0.076923  p[4] 0.076923  p[5] 0.076923
p[6] 0.076923  p[7] 0.062937  p[8] 0.083916  p[9] 0.083916  p[10] 0.30769
Hope that helps in explaining what I'm up to.
k_c