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.....
Z-scores
- Thread starter mjbballar23
- Start date
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-
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...
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.
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.
z scores
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)
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)
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.
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 scores
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.
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.
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.
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.
z scores
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.
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.
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-
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-
Yeah. I’ll have a general idea of what my EV is before I sit down to play, but then I’ll adjust that based on the actual conditions in the casino. For example, if the dealer is slow then I’ll adjust the hands per hour so that the results are a bit closer. If I spent most of the session scouting for tables then I’ll adjust the playing time to reflect that.
It’s easy to be off but it usually isn’t by much. A small margin of error is to be expected when dealing with deviations. These are just estimates anyway so you should look at them as broad brush strokes of the big picture. I just look at my z-score for a short-term range like a week or so, or just a particular trip. It will give me an idea of how unusual that “slice” of my life was. I don’t look at long-term z-scores because I don’t think my records are detailed enough to give accurate results over an extended period of time.
-Sonny-
It’s easy to be off but it usually isn’t by much. A small margin of error is to be expected when dealing with deviations. These are just estimates anyway so you should look at them as broad brush strokes of the big picture. I just look at my z-score for a short-term range like a week or so, or just a particular trip. It will give me an idea of how unusual that “slice” of my life was. I don’t look at long-term z-scores because I don’t think my records are detailed enough to give accurate results over an extended period of time.
-Sonny-
Sonny said:
Now he’s only off by 1.35 SDs, which is a much happier circumstance.
If it reaches -3 it's time to take a serious look at what you're doing! Sure it might just be extreme variance, but you'd better be sure. It's far too easy to just shrug it off without thinking about it. A -3 z-score isn't definitive proof of anything, but it is still cause for concern.
I’ve certainly made my share of bone-headed plays in my day. I’d rather figure it out at –1.96 than at –3.
Very true, but knowing that the big picture isn't so bad makes it easier to hit the tables again. The money comes and goes. That’s just part of the game. Seeing that what seemed like a big loss was actually just a small bump can help smooth out the emotional part of the game. Sometimes it's the only comfort you're going to get.
-Sonny-
I’ve certainly made my share of bone-headed plays in my day. I’d rather figure it out at –1.96 than at –3.
Very true, but knowing that the big picture isn't so bad makes it easier to hit the tables again. The money comes and goes. That’s just part of the game. Seeing that what seemed like a big loss was actually just a small bump can help smooth out the emotional part of the game. Sometimes it's the only comfort you're going to get.
-Sonny-
I had a suspicion you might be doing what you did - because I tend to do the same thing.
Maybe it's because the stan dev is in dollars not units.
So, in dollars, it's $27.50/16.37=1.68 avg bet units per hand.
How he got that $275.09, or avg bet for that matter, I don't know either. When I try to figure SD in terms of units, I don't seem to come close.
Sonny, anyone, is it possible to figure that out from the info given? Or is just the result of sims? It just seems I should be able to corroborate win rate and avg bet at least?
Maybe it's because the stan dev is in dollars not units.
So, in dollars, it's $27.50/16.37=1.68 avg bet units per hand.
How he got that $275.09, or avg bet for that matter, I don't know either. When I try to figure SD in terms of units, I don't seem to come close.
Sonny, anyone, is it possible to figure that out from the info given? Or is just the result of sims? It just seems I should be able to corroborate win rate and avg bet at least?
BTW, thanks for taking the time to answer that other question so at least I know I got that much right lol.
That's interesting you do it frequently but not globally. Makes sense too lol.
Anyway, maybe estimates might not make for big errors but I guess wrong methodolgy could?
Are you saying you basically figure things out per hand and work from there?
That's what makes the most sense to me anyway.
Although I can see why one wants to compare win/hr rather than win/hand.
I guess what always strikes me is understanding the underlying assumptions of a sim. Like in Schlesinger's case, I guess there's x players at the table, the TC is truncated not rounded, it's based on a half-deck estimate, bets are jumped when required, I18 is used and maybe Fab 4 if LS is offered along with a certain amount at a certain TC.
So alot of things that one might not be doing in real life lol.
That's interesting you do it frequently but not globally. Makes sense too lol.
Anyway, maybe estimates might not make for big errors but I guess wrong methodolgy could?
Are you saying you basically figure things out per hand and work from there?
That's what makes the most sense to me anyway.
Although I can see why one wants to compare win/hr rather than win/hand.
I guess what always strikes me is understanding the underlying assumptions of a sim. Like in Schlesinger's case, I guess there's x players at the table, the TC is truncated not rounded, it's based on a half-deck estimate, bets are jumped when required, I18 is used and maybe Fab 4 if LS is offered along with a certain amount at a certain TC.
So alot of things that one might not be doing in real life lol.