SD check my math

This goes back to an earlier message that I wrote but wanted to do a little more research. I am not concerned about the amount wagered but more interested in the time it would take to at least break even with the worst of luck.

Lets say you are betting $100 per hand with a 1% advantage. I decided to calculate the SD and find out at what level you would break even if you had just terrible luck.

So if you play 50,000 hands the SD is square root of 50k = 224 x 1.1 = 246.4 units at 1SD. 2SD would bring you to 492.8 for 95% of the time. I know there are 3SD but I am just basing it off of 95% of the time. So basically you have 493 units fluctation x $100 per hand is $49,300. If you have a 1% advantage and play 50,000 hands at $100/hand, the EV is $50,000. This number is greater than the fluctuation of $49,300 which would mean that at worst case you would be break even or better 95% of the time. If you played 100 hands per hour, it would take you 500 hours which is a very very long time. It would be pretty depressing if you had to play that long to get back to even. I know rules and play have a big thing to do with it but just assuming that you play average to good rules with perfect BS play with some index incorporated too.

Did I calculate this right? Again, I don't plan on playing as long or at this level but more just wanted to learn how long to break even at 95% of the time. Also this just reaffirms how dramatic the swings can be.

Thanks,
Brendan

In fact, you'll be within 2 SD roughly 95% of the time, which means that on 5% of the time you'll do either better or worse than these 2 SD. Since half of this 5% (2.5%) will be on the positive side, only 2.5% of the time you'll do worse than 2 SD.

Conclusion, you can say that after 500 hours, your result will be even or better 97.5% of the time. Assuming EV and SD as stated.

I was playing the SD at Turning Stone back in the good ole days, dead even game off the top. During one trip, spreading 1-5 quarters, I dropped over $14K in about a week. I drove home, grabbed a stack of money, and drove straight back. Over the next 3 weeks I won over $18K. Fired up the laptop and determined I would have a swing like that about once every 40 years. Figured the next 39 years, 51 weeks were a freeroll.

Are you really FLAT BETTING $100 a hand with a 1% advantage? I'm not sure just how you would accomplish that.

If, instead, there is some sort of a spread, or if $100 is your average bet per hand, then you can't just use 1.1 (1.14, in any case) to multiply. Your s.d. will be much larger than what you think it is.

Don

Don,

As if he didn�t think things were bad enough, you made him realize that his standard deviation is much larger than he thought. At least GMan had some good news for him (1/2 of the time his greater than 2 standard deviation result is on the �good� side of the curve).

Dr 21

Hey, I don't make the laws; I just report them! :-)

Don

"spreading 1-5 quarters, I dropped over $14K in about a week. I would have a swing like that about once every 40 years."

That is only 112 top bets. You will have those kind of fluctuations
more often than that. Sorry...

I did the math.

I come close to losing my entire session bankroll (usually 9k) about one time in thirty.When I experienced my first severe medium term down swing (-50k)I also figured it wood remain the only time this occurred in my career ... but it has happened again since!
The other side: just recently I won 16k within two hours, a new personal record (max bet was 3*200).
A tip: for the calculation of sd you should consider max bet and its frequency rather than average bet.

Francis Salmon

you have no idea how often I play the game, what count I sit out at, etc. Like I said, I did the math.

As long as you don't post details, we have to make assumptions and according to these assumptions I figured that your loss was slightly more than 2 sd: that means it occurs once in 50 week-trips.

Francis Salmon