Unexpected standard deviation value

[mhluska]

The current output for standard deviation seems to be the standard deviation for earnings per hand. This empirical number doesn't seem to line up with the equations. For example:

$ blackjack-simulator simulate --minimum-bet '$25'

Table Rules:    $25–$2,500 2D 3:2 H17 DAS NLS NRSA
Penetration:    75.00%
Bet Spread:     TC 0: $25, TC 1: $50, TC 2: $100, TC 3: $200, TC 4+: $400
Spots Played:   TC 0+: 1
Bankroll Rqd:   $36,026.41 (5.00% RoR)
Expected Value: $255.97/hour
Std Deviation:  $171.63
House Edge:     -1.42%
Hands Played:   10M
Amount Earned:  $12,247,462.50
Amount Wagered: $860,190,225.00
Hands Lost:     4.8M
Hands Pushed:   820.7K
Hands Won:      4.4M
Time Elapsed:   1.78 seconds

So sd is $171.63 per hand if we're spreading $25-$400 over 10M hands. That already seems unusual.

sd = 1.1 * sqrt(N) = 1.1 * sqrt(10M) = 3478.51 units. If our average bet or unit here is $86, then we're looking at a total sd of $299,851 after playing 10M hands.

I'm not really sure how to reconcile that number with our $171.63 value. If the value is correct, it seems to say that s.d. per hand for us is 1.99 whereas BJA says it should be 1.15 or 1.11. This could be entirely due to our aggressive (and imperfect) bet spread.

So things to do:

• Revisit this value after calculating an optimal bet spread and see if it aligns more closely with 1.1
• Add "per hand" to the output to make it clearer what it represents
• Maybe add an average bet size to the output too