Help! What's wrong with this math?

[ezinestein]

Hi,

I hate sounding so stupid... but I really want to know how to figure this stuff out.

I’m trying to figure out how to figure out the Standard Deviation when playing blackjack. Can anyone please tell me if this is the right way to do it?

Example:

1. Playing a game where the house has a 0.5% advantage.
2. 400 hands at $5 per hand for a total of $2000 wagered.

1.1 / 20 (20 being the square root of 400) = 0.055
0.055 * 400 hands = 22 units
22 * $5 bets = $110
So... $110 equals one standard deviation... right?

So with the -0.5% EV of $10... would your numbers for 1 standard deviation be... -$120 to +$100?

So if you started with a $200 bank roll you could end up with anywhere between $80 and $300? Is that right?

And 2 standard deviations would be ‘bust’ on the low end or $410 on the high end right?

Thank you for any help with figuring this stuff out.

Kindly,
Ezinestein

PS – Also... can anyone direct me to something that shows me how to easily figure out risk of ruin... and how to figure out what size bank roll a person needs depending on bet size?

[driller]

If you will go to the "Essays" section you will see that Mason has written an essay on computing standard deviation.

I'm far from a math or probability whiz, but I don't think sd depends on ev. It is computed from actual results.

In conjuction with ev, sd can be used to calculate a gambler's chance of ruin and other things which can be helpful in bankroll management.

[Leo99]

I don't think it's that simple. Maybe BJ might be that simple but only if your EV is constant for each play. Take a slot machine or VP. Two VP games might be -0.5% but one takes, takes, takes then has a big payout, while the other VP game might take a little, give a little without any big swings. You need to calculate SD from actual numbers for poker but you should be able to calculate a theoretical SD for as you keep your bets constant. I wish I knew how to do that ;-) Oh, I know how to keep my bets constant it's the math I forget.

[Vintage]

simple

[blank frank]

[ QUOTE ]

I’m trying to figure out how to figure out the Standard Deviation when playing blackjack. Can anyone please tell me if this is the right way to do it?

Example:

1. Playing a game where the house has a 0.5% advantage.
2. 400 hands at $5 per hand for a total of $2000 wagered.

[/ QUOTE ]

Now, I'm not totally up on blackjack, so I may be misinterpreting this. If you assume each hand is independent, and you have a 49.5% chance of winning each one (that's how I interpret 0.5% house advantage), you expect to win n*p hands (400 * 0.495 = 198). Your variance on that is n*p*q where q=1-p (400 * 0.495 * 0.505 = 99.99). Your standard deviation is the square root of the variance, or 9.9995. Call it 10 and you've got a confidence interval of 178 to 218 wins. With +/- $5 as the outcome, that translates to results from losing $110 to winning $90.