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  #1  
Old 01-19-2005, 11:57 PM
bisonbison bisonbison is offline
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Default Plotting a distribution of expected session outcomes.

I've got an idea but not enough knowledge of excel to know if it's possible, and I was thinking you prob guys are probably the ones to ask.

Basically, using the SD equation from Homer's streaks thread, I'd like to be able to plot a bell curve of outcomes from X sessions of Y hands.

In other words, given that my win-rate is BlahBlahBlah and my SD is poop, what are the range of session outcomes I can expect to see over 10k sessions?
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  #2  
Old 01-20-2005, 12:14 AM
sthief09 sthief09 is offline
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Default Re: Plotting a distribution of expected session outcomes.

[ QUOTE ]
I've got an idea but not enough knowledge of excel to know if it's possible, and I was thinking you prob guys are probably the ones to ask.

Basically, using the SD equation from Homer's streaks thread, I'd like to have to be able to plot a bell curve of outcomes from X sessions of Y hands.

In other words, given that my win-rate is BlahBlahBlah and my SD is poop, what are the range of session outcomes I can expect to see over 10k sessions?

[/ QUOTE ]


I tried to search for it, but to no avail. Homer posted an Excel spreadsheet that does exactly this recently. try PM'ing him, or maybe your search skills are better than mine. he posted it in the zoo
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  #3  
Old 01-20-2005, 12:31 AM
bisonbison bisonbison is offline
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Default Re: Plotting a distribution of expected session outcomes.

I found it:

Homer's Other Streaks Thread

I'm not sure if this does exactly what I'm after but it sure is neat.
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  #4  
Old 01-20-2005, 01:39 AM
gaming_mouse gaming_mouse is offline
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Default Re: Plotting a distribution of expected session outcomes.

Cool link, bison. thanks.

Hope it wasn't prompted by a downswing.

gm
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  #5  
Old 01-20-2005, 01:41 AM
bisonbison bisonbison is offline
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Default Re: Plotting a distribution of expected session outcomes.

meh, I don't believe in downswings.
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  #6  
Old 01-21-2005, 04:02 PM
That guy That guy is offline
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Default Re: Plotting a distribution of expected session outcomes.


I am no stats guru but if memory serves me right:

If you have the Std Dev and you can assume 'normality' in the distribution,

If you are +2 BB's per session (consisting of say 95 hands)
you can run a simple confidence interval where;

+1 SD = 2bb's + 18bb's
-1 SD = 2bb's - 18bb's

playing at 3/6 =
12 + 108 = +$120
12 - 108 = -$96

Any session should fall within a -$96 to +$120 band, with ~68% confidence

You have 84% confidence that your next session will not lose more than $-96. Thus you will lose more than -$96 about 16% of the time.

95% of sessions should fall within 1.65 standard deviations
(-$166 to +$190).
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  #7  
Old 01-21-2005, 08:22 PM
yoshi_yoshi yoshi_yoshi is offline
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Default Re: Plotting a distribution of expected session outcomes.

I'm not sure about excel, but you can easily plot the graph on a graphing calculator or a computer program if you have one.

The formula is:

P(x)= [e^(-((x - EV)^2)/(2*SD^2))] / (SD * sqrt(2*pi))

You should get a nice looking bell shaped curve, centered at your EV.

For more info, normal distribution
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  #8  
Old 01-22-2005, 01:55 PM
Little Lew Little Lew is offline
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Default Re: Plotting a distribution of expected session outcomes.

Confessing some experience with experimental stats in prior life ---------

I don't think that you can make any assumption of normality in the distribution of the bb/hr or bb/session figures because, unless the player is incredibly disciplined, the player will react to losing or winning streaks by changing behavior- perhaps to limit losses or pressing to maximize gains.

Since you have all the the session figures, it would be optimal to actually chart all the session figures and see if these figures are actually distributed normally. Once you are convinced that the figures are normally distributed then you can have confidence in the estimates of possible per session gains/losses.

A link to a discussion on skewness (the degree of asymetry of a distribution) or kurtosis ( the excess peakedness or flatness of a distribution) is at

overtechnical blather on kurtosis/skewness

My intuition is that my own results would be greatly skewed because I am perfectly happy to win as much as I can (on the rare occasions I actually win) but I tend to tighten up, sulk and even leave when my losses get too high at any session. (Actually it is fear of my spuse looking over my shoulder and then clutching my neck.) [img]/images/graemlins/smile.gif[/img]
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  #9  
Old 01-22-2005, 05:34 PM
That guy That guy is offline
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Default Re: Plotting a distribution of expected session outcomes.

Monte Carlo analysis do not need the assumption of normality so the original post is very valid.
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  #10  
Old 01-24-2005, 01:41 PM
Analyst Analyst is offline
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Default Re: Plotting a distribution of expected session outcomes.

[ QUOTE ]
I've got an idea but not enough knowledge of excel to know if it's possible, and I was thinking you prob guys are probably the ones to ask.

Basically, using the SD equation from Homer's streaks thread, I'd like to be able to plot a bell curve of outcomes from X sessions of Y hands.

In other words, given that my win-rate is BlahBlahBlah and my SD is poop, what are the range of session outcomes I can expect to see over 10k sessions?

[/ QUOTE ]

Interesting - I was just thinking about this topic this morning after a massively bad run last night. The magnitude of upswings and downswings (mainly the latter) is a frequent topic on the HUSH board.

The key issue, I think, is that session results are ultra-short runs and may very well not fall into a normal distribution. Yes, when you add them up in the long run, the law of large numbers takes over and your total results will be approximately normally distributed. However, as we all know the long run is, well, long - perhaps hundreds of thousands of hands or even more while a single session is very short indeed (well, it seemed pretty long last night. [img]/images/graemlins/frown.gif[/img] )

Basically, I'm beginning to think it is completely unrealistic to say "My win rate is X/100 hands with a SD of Y/100 hands, so I should expect ~2/3 of my 100-hand sessions to fall in the range of X +/- Y."

To address your question, yes, I think there is a way to model this with Excel using Monte Carlo simulation. Complex and tedious, but worthwhile study and I'm thinking about how to structure it. A bigger hand database than mine would be helpful - want to collaberate?
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