Z-scores

[mjbballar23]

does anyone else calculate the Z-score for their results? Right now my z-score is -1.34. Kinda frusturating when i think about where i'd be sitting if my z-score was +1.34. I'm starting to believe that i might not be getting as many hands per hour as i thought and that might be a big comtributor to this. Im kinda curious to hear where other people are sitting with their results.....

[Sonny]

Using z-scores can be a good way to see how close you are to your expectation. Sometimes after a huge losing session I might feel pretty bad, but when I see the z-score or my overall results in units it helps to settle my nerves. Sometimes a lot of money only adds up to a small change in your results. That can help take some of the sting out of the extreme variance.

Also, z-scores can be used to find out fun things like your probability of being ahead for a given period. That's another good way to get peace-of-mind in the gambling world.

-Sonny-

[mjbballar23]

Originally Posted by Sonny

Using z-scores can be a good way to see how close you are to your expectation. Sometimes after a huge losing session I might feel pretty bad, but when I see the z-score or my overall results in units it helps to settle my nerves. Sometimes a lot of money only adds up to a small change in your results. That can help take some of the sting out of the extreme variance.

Also, z-scores can be used to find out fun things like your probability of being ahead for a given period. That's another good way to get peace-of-mind in the gambling world.

-Sonny-

sonny i couldn't of said it better myself. Whenever i feel like something funny is going on with my results, i just look at my z-score and realize that im still well within the expected variance for the game. Although -1.34 is somewhat unusual it is definitely not unheard of. If it ever gets below -2, thats when ill start to rethink things...

[Kasi]

Originally Posted by mjbballar23

does anyone else calculate the Z-score for their results? .

The z-score is the same thing as standard deviation right?

Anyway, I used to and I'd have a different one for every different game. Obviously things like win/hand and standard deviation can change from one game to the next.

So, when you say you only have one z-score does that mean you 've always played the same game in about the same way?

If not, is it some average?

So maybe figure out a range based on a low and high number of hands, etc.

But I think you're doing the right thing to examine things in more detail just in case.

Maybe, if you're already not, going forward, try figuring it out maybe more often, maybe even by session, forcing you to perhaps specify exp win rate, hands played ,etc.

[mjbballar23]

Originally Posted by Kasi

The z-score is the same thing as standard deviation right?

Anyway, I used to and I'd have a different one for every different game. Obviously things like win/hand and standard deviation can change from one game to the next.

So, when you say you only have one z-score does that mean you 've always played the same game in about the same way?

If not, is it some average?

So maybe figure out a range based on a low and high number of hands, etc.

But I think you're doing the right thing to examine things in more detail just in case.

Maybe, if you're already not, going forward, try figuring it out maybe more often, maybe even by session, forcing you to perhaps specify exp win rate, hands played ,etc.

yea a z-score is the number of standard deviations you are from your EV. Statistically, anything lower than -2 or higher than +2 is concidered unusual. I am gonna try and be more specific about logging the playing conditions from session to session. And yes i do play about the same game in about the same way; however, you should be able to combine all your results into one z-score because Expected Values can be added and standard deviations add after you square each of them.(aka variances add)

[Kasi]

Originally Posted by Sonny

Using z-scores can be a good way to see how close you are to your expectation. Sometimes after a huge losing session I might feel pretty bad, but when I see the z-score or my overall results in units it helps to settle my nerves.-Sonny-

You know the more I think about the more I wonder how you/or anyone does go about figuring your z-score.

I mean do you do it in units or dollars or something per hour or perhaps by hand? Is knowing your average bet important because that would be the unit you would need to figure how bad/good a dollar loss is?

Do you just estimate an overall average win rate - from sims or otherwise?

Would it be pretty easy to be way off with some wrong estimates?

And what kind of gyrations do u have to thru, if any lol, to maybe combine results?

I mean it seems it's not exactly easy to figure out.

[mjbballar23]

Originally Posted by Kasi

You know the more I think about the more I wonder how you/or anyone does go about figuring your z-score.

I mean do you do it in units or dollars or something per hour or perhaps by hand? Is knowing your average bet important because that would be the unit you would need to figure how bad/good a dollar loss is?

Do you just estimate an overall average win rate - from sims or otherwise?

Would it be pretty easy to be way off with some wrong estimates?

And what kind of gyrations do u have to thru, if any lol, to maybe combine results?

I mean it seems it's not exactly easy to figure out.

Z-SCORE= ((ACTUAL RESULTS IN $) - (EXPECTED RESULTS IN $)) DIVIDED BY(STANDARD DEVIATION FOR THE # OF HANDS PLAYED)

EXPECTED RESULTS = HOURLY EXPECTATION * # OF HOURS PLAYED
STANDARD DEVIATION = STANDARD DEVIATION PER HAND*SQUARE ROOT(# OF HANDS PLAYED)
STANDARD DEVIATION PER HAND = AVERAGE BET * 1.15(FOR 1 HAND), 1.35(FOR PLAYING 2 SIMULTANEOUS HANDS), OR 1.54(FOR PLAYING 3 SIMULTANEOUS HANDS)

Its much more difficult to figure out if you play about alot of different casinos with varying rules, hands per hour, and degrees of penetration. I calculate my z-score based on a per 100 hands win rate(approximately 1 hour worth of play). Calculating it requieres a frequency distribution of TCs at the penetration level you receive(a lot of books have them/simulators have them as well) and using that to figure out your average bet, and hourly expectation. I programmed all the calculations into an Excel graph one day and it does all the work for me now. I like knowing my z-score because it really helps you realize after a bad day that it is all within the expected variance for the game. Sorry if this is somewhat confusing, I couldn't think of a better way to explain it. If anyone has a better way of explaining this that would be great.

[Kasi]

Originally Posted by mjbballar23

Z-SCORE= ((ACTUAL RESULTS IN $) - (EXPECTED RESULTS IN $)) DIVIDED BY(STANDARD DEVIATION FOR THE # OF HANDS PLAYED)

EXPECTED RESULTS = HOURLY EXPECTATION * # OF HOURS PLAYED
STANDARD DEVIATION = STANDARD DEVIATION PER HAND*SQUARE ROOT(# OF HANDS PLAYED)
STANDARD DEVIATION PER HAND = AVERAGE BET * 1.15(FOR 1 HAND), 1.35(FOR PLAYING 2 SIMULTANEOUS HANDS), OR 1.54(FOR PLAYING 3 SIMULTANEOUS HANDS)

Thanks mj. I appreciate your explanation.

So, I'll just take a line from BJ Attack that I assume might be similar to how a sim might express the results.

It says for a 6/8 S17 DAS with a play-all 1-8 spread, the optimum min bet is 1354 units with a $10K roll, avg bet $16.37, W/L %=0.46 and SD/100=$275.09and $7.56 win per 100.

Is that enough info, or the kind of info you use, to figure out one's z-score?

To make a long story short and help me decide whether I'm crazy, given the above, if I am down $1095 dollars after 1000 hands, would that be about a -1.34 z-score?

Put another way, if I want to relate my loss to average-bet units, it'd be like 67 units down with a stan dev of 1.66/hand instead of the 1.15 I'm more used to?

No big deal - I do better in figuring out where I might be going wrong by using real numbers rather than x's and y's lol.

[mjbballar23]

Originally Posted by Kasi

Thanks mj. I appreciate your explanation.

So, I'll just take a line from BJ Attack that I assume might be similar to how a sim might express the results.

It says for a 6/8 S17 DAS with a play-all 1-8 spread, the optimum min bet is 1354 units with a $10K roll, avg bet $16.37, W/L %=0.46 and SD/100=$275.09and $7.56 win per 100.

Is that enough info, or the kind of info you use, to figure out one's z-score?

To make a long story short and help me decide whether I'm crazy, given the above, if I am down $1095 dollars after 1000 hands, would that be about a -1.34 z-score?

Put another way, if I want to relate my loss to average-bet units, it'd be like 67 units down with a stan dev of 1.66/hand instead of the 1.15 I'm more used to?

No big deal - I do better in figuring out where I might be going wrong by using real numbers rather than x's and y's lol.

Thats exactly the info you need. Heres how i interpret your results. With an average bet of $16.37, your standard deviation per hand is 16.37*1.15 = $18.83. Your standard deviation for 1000 hands is 18.83*square root(1000) = $595.46. After 1000 hands you expect to be up $7.56*10 = $75.60. so:
Z-score = ($-1095-$75.60)/595.46 = -1.966
That z-score is for only playing one hand. -1.966 is very low and is getting to the point where you might reevaluate the game you are playing. Your z-score for playing two hands is -1.675, which is still low but definitely not unheard of. The only thing I dont understand about the numbers from Blackjack Attack is how it got a SD/100 hands = $275.09. I dont know why it would calulate your SD per hand to be 1.68*average bet, unless you were playing 4 hands or something. Ill have to take a look at the book myself and figure it out. Hope this helps.

[Sonny]

Originally Posted by mjbballar23

The only thing I dont understand about the numbers from Blackjack Attack is how it got a SD/100 hands = $275.09.

It probably has to do with the bet spread. Since he is making bigger bets when the variance is slightly higher, the overall SD will tend to cluster around those big bets. In that case we would expect the SD to be higher than the average bet. In any case, if we use a SD/hand of 27.5 we get much different results:

z = (-1095-75.6)/(27.5 * sqrt(1000))
z = -1170.6/869.6
z = -1.35

Now he’s only off by 1.35 SDs, which is a much happier circumstance.

-Sonny-