Calculating Standard Deviation in Blackjack


Dormant account
Oct 8, 2002
Hi all,
I'm working on a little project to quantify how good casino offers are. The end result will show for each offer, given the type of blackjack being played (e.g. 6 decks, no double after split, split on 9,10,11, no blackjack checker and assuming basic strategy) a number of probabilities.

The probabilities I would like to be able to calculate are:
1. What is the chance of losing more than your deposit
2. What is the likely range of your expected net profit/loss given n number of hands.
3. What is the chance of making x amount of profit - eg $100.

I'm part way there with it (de-rusting my statistics in the process) but need an accurate way of calculating the standard deviation for any given ruleset of blackjack and the number of hands played.

Is there a free-ware simulator that anyone's aware of that I might be able to use for this?

Is there any other way of doing it?

I can calculate the house edge from The Wizard of Odds' Old / Expired Link but I'm not sure it's just a case of plugging this figure in to work out the standard deviation as there are probabilities for pushes, 2 unit wins, 2 unit losses etc to consider as well as the probability of just success or failure (like a coin flip).

I am happy to publish my workings/results back to this board as I go along if there is any interest in this and would be grateful for any help that you may provide.

many thanks,
Well, if you read my post in "Wildcards" you'd know about my relationship with mathematics. :)
Spearmaster might be able to give you a little guidance since he's a "visual mathematician" (whatever the hell that means). I guess he has the ability to do math in his head (card counting perhaps? ha!)

Yes, please post your findings here. Even us who are math numb would benefit from the read.

If you have Excel, the Wizard of Odds has published a formula that you can plug into it in order to determine the information you'd like. He uses an SD of 1.16 per hand and I think you'll find that will suffice for most games. I have seldom seen it below 1.10 or over 1.30, and most fall in that 1.15-1.18 range. There is more info. on his site about that, here: Old / Expired Link

But back to the calculations. I just went over to his site to find the article, but couldn't. I'm sure it's in there somewhere, though and it may be an answer to one of his reader's questions. Go there and poke around some.

Hi gamesmaster,
Having had a little dig around I found exactly what you were talking about in his FAQ section Old / Expired Link - the last question answers it and gives the Excel calculations too. Thanks for the tip!

Now, back to my spreadsheet and the brain-ache,


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