Standard Deviation

I posted about this a long time ago and wanted to review the topic.

I would assume I could be about 95% sure of having an even or winning game if I was was a least two Standard Deviations in winnings above zero after x hours of play correct?

I was wondering how we figured average bet on say a 6D H17 DAS game one other player average Surrender Aces split four times? Spreading 5 to 100 on one hand. 85 pen. Skies fairly cloudy; 20% chance of precipitation.

Wonging out at TC-2 half the time.

If I deserve flaming then fire me up. Nietzsche said it is a disservice to not punish the guilty.

that doesn't sound right. I'm not a math genius, but it looks like your question doesn't make sense. I think you're trying to say that you would have a 95% chance of being within 2SD after X hours. that is plus or minus SD.

I think if you want to figure out if you're playing within expectation, it is better to use your simulated win rate/hr and compare it with your actual logged hours and BR growth.

I will look up NO later on but:

If 95% of the time you are within 2SD of your expected value it should follow that if you are 2SD over an EV of anything over zero you can be 95% sure you are playing a winning game.

If I play 100 hands at an EV of zero with an average bet of 10 it follows 1.15 x SQRT(100) x 10 = $115 which should be one SD. If I was anywhere between $230 or -$230 which is 2SD that would be the range I would find myself in 95% of the time in this simple example.

ehhhhh, that's kinda what I said. at least the second part is. The first part however, is meaningless. The concept of being within 2SD, 95% of the time is really, really, really, really general. You can't be sure if you're playing a winning game if you're looking within a scope of that size. That's like saying, I'm a pro heads/tails coin flipper because I either make $1000 or lose $1000. Actually, I'll take a great example from the book "the quants" starring Ed friggin Thorp.

As part of the interview process for a particular quant fund, applicants are asked a simple question by the interviewer. "what amount could you say with a 95% certainty is the amount of cash I have in my pocket right now." applicants who would guess $100, $200, 3, 4, $500 would be wrong. The answer was: "anywhere between $0-$10,000. It's the only way to be 95% certain."

SD only shows a range of outcomes possible set forth by user defined parameters, nothing more. If you want to check and see if you're playing a winning game, you have to take meticulous notes. If your simulated win rate is $50/hr, but your last session you walked off with $1000 extra in a 3 hour time frame, you have to visualize it as: "I made $150 of real BR growth. I also got lucky and won $850 extra." Likewise, if you lost $1000 in 3 hours, you have to think, I made $150 of +ev choices, but I hit a negative swing of $1000. No sweat, just wait for the next session.

N0 is a concept of determining how many hands it will take you to overcome 1SD of "luck" and experience real winrate growth. The lower the number, the better. Sonny got a post of the month award for his thorough explanation of it.

http://www.blackjackinfo.com/bb/showpost.php?p=28936&postcount=3

Thanks Jack and Flash I appreciate your valuable time in answering my post. The NO post by Sonny looks very interesting. I have some good information to study now.

Good Variance