BS vs. AP after 230 hrs?

nottooshabby

Well-Known Member
#1
Please help me settle a gentleman's (and I use that term loosely) bet. I have kept meticulous records of my last 230 hrs with a modest profit (hey, I'm not complaining . . . I've had to dig out of some pretty deep holes!) One of the guys I work with believes that a purely BS player flat betting can also come out ahead of the game after 230 hrs, although he agrees it would be an extremely rare occurence. What are the chances of this?
 

callipygian

Well-Known Member
#2
nottooshabby said:
One of the guys I work with believes that a purely BS player flat betting can also come out ahead of the game after 230 hrs, although he agrees it would be an extremely rare occurence. What are the chances of this?
The standard deviation for one hand, BS flat betting is about 1.15 units. So, at 230 hours around 100 hands/hr and an EV of -0.005, you should have -115 +/- 174 units. There's a 25% chance (z = 0.66) of you coming out ahead.

The problem is that if you're spreading your bets, your standard deviation is higher than 1.15 units, and can be 2 to 3 units per hand. This actually increases the chances of coming out ahead purely by chance - given that you randomly increase your bets, your EV will remain the same but your variance will increase. At a SD of 2 units per hand, you had a 35% (z = 0.38) chance of coming out ahead, and at a SD of 3 units per hand, you had a 40% (z = 0.25) chance of coming out ahead.

Can you post the number of units you are up and your bet ramp? I could calculate the probability you'd be up by as much as you are up now, and your variance.
 

callipygian

Well-Known Member
#5
Dang it, that's a hard variance to calculate. I'll just tell you how to calculate this percentage, and you can try to calculate your variance on your own.

(1) Take the number of units above basic strategy EV. So, in the case where I was looking at breaking even, that would be 0 - (-115) = 115 units above expectation.

(2) Estimate your standard deviation by multiplying the standard deviation per hand (probably between 2 and 3) by the square root of hands played. So, in the case where I estimated your SD/hand at 3, your SD was 3*sqrt(230*100) = 455 units.

(3) The answer from (1) divided by the answer from (2) is your z score - it's a mathematical expression of how far you are from the mean, measured in SD's. So in the previous example, z = 115/455 = 0.253.

(4) You can convert z to a probability using free calculators on the Web (it's a mathematical function, so there's an exact formula if you want too). I used the first one that came up by Googling "z score calculator" - http://www.fourmilab.ch/rpkp/experiments/analysis/zCalc.html. z = 0.253 corresponds to probability (Q) = 0.400, or 40%.

You can do these steps with your actual winnings and actual SD once you figure out your actual SD. It's not trivial, but straightforward. If you look at Prince Dragon's attachment, the SD (Std Dev) is listed just to the right of the Results (EV). Remember to normalize everything to units or dollars, but don't mix both.
 
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