U
Ubercroz
Visionary
Silver Level
whew, looks like I was not too far off the mark.
Interesting musing.
However if you were to run that 99 below EV over a large sample size, it would be like a statistical miracle - since it should be so far outside of the standard deviation that it would be nearly impossible.
Interesting musing.
However if you were to run that 99 below EV over a large sample size, it would be like a statistical miracle - since it should be so far outside of the standard deviation that it would be nearly impossible.
U
Ubercroz
Visionary
Silver Level
Exactly that, the point stands the higher your EV the higher potential 'under EV' you have.
So while it would be nuts to run 99 below EV, it would not be that unusual to be at 65% EV and run at, say 45%. The closer it gets to even the more you can expect to run below your EV, the higher EV you have the more potential there is to not meet your expectation (though it should be rare).
So while it would be nuts to run 99 below EV, it would not be that unusual to be at 65% EV and run at, say 45%. The closer it gets to even the more you can expect to run below your EV, the higher EV you have the more potential there is to not meet your expectation (though it should be rare).
duggs
Killing me softly
Silver Level
It's not much that its more common more that it's more widely spread, running slightly below EV is less common than running slightly above EV but running way below EV is more common than running way above EV
duggs
Killing me softly
Silver Level
I think iv tweeted hand drawn ones at Nate meyvis a few times, lol
U
Ubercroz
Visionary
Silver Level
Good clarification, thanks.
Matt Vaughan
King of Moody Rants
Bronze Level
This.
vinylspiros
PIRANHA-------->< (((º>
Silver Level
Just went through the whole thread. Have nothing to add . Just wanted to say that you guys are nuts.OH,, and im never going to sit at a cash table with any of you. taking things to new levels here with this scientific stuff. got us normal people panicking that we are slow.
Mr Sandbag
Legend
Silver Level
Just went through the whole thread. Have nothing to add . Just wanted to say that you guys are nuts.OH,, and im never going to sit at a cash table with any of you. taking things to new levels here with this scientific stuff. got us normal people panicking that we are slow.
I know, right? F**k...
hackmeplz
Sleep Faster
Silver Level
We flip 100 times for $1, win 80%. Obviously our ev is $80. We win all 100 0.8^100, how often do we win 60? I think as the number of samples gets high enough (what's high enough?) it becomes closer and closer to a normal curve vs. a skewed curve such that it should be pretty equally likely to run above or below ev. I've got other school stuff to do now but when I'm done I might write a quick program to run simulations on this.
hackmeplz
Sleep Faster
Silver Level
Like obviously it will never be a perfect normal distrubution because of the upper bound on how good you can run being a lower distance from the mean than the lower bound but as you have more and more samples there becomes an effective lower bound as going below it begins to be running 20+ standard deviations below the mean which just doesn't happen lol.
Logan2
Legend
Silver Level
I don´t get why bigger pot means bigger variance?.
If in a 50bb pot we are 70% favorite, and in a 200bb pot we are 70% favorite, variance should be the same no matter pot amount. What i missing?
Sure $ difference on ev would be higher with bigger pot but i don´t see why variance should not be the same??
Matt Vaughan
King of Moody Rants
Bronze Level
I mean, it's still a binomial distribution, so it's not like it's some vague, unknown distribution where we desperately need to use the central limit theorem. But if it makes you happy
http://en.wikipedia.org/wiki/Binomial_distribution
"If n is large enough, then the skew of the distribution is not too great. In this case a reasonable approximation to B(n, p) is given by the normal distribution
N(np, np(1 - p)),
and this basic approximation can be improved in a simple way by using a suitable continuity correction. The basic approximation generally improves as n increases (at least 20) and is better when p is not near to 0 or 1."
hackmeplz
Sleep Faster
Silver Level
In a 50bb pot we will either win 50bb or win 0bb with a mean of 35. This means we will either have a deviation of 35 or 15bb from the mean.
In a 200bb pot we will either win 200 or 0 with a mean of 140. This means we will either have a deviation of 140 or 60 from the mean.
The mathematical definition of variance (according to wikipedia anyway) is:
"the expected value of the squared deviation from the mean μ = E[X]:"
So I think it's safe to say that the value of the square of the difference from the mean in #1 will always be less than in #2, therefore the expectation must be smaller, thus the variance will be smaller.
hackmeplz
Sleep Faster
Silver Level
I mean, it's still a binomial distribution, so it's not like it's some vague, unknown distribution where we desperately need to use the central limit theorem. But if it makes you happy
http://en.wikipedia.org/wiki/Binomial_distribution
"If n is large enough, then the skew of the distribution is not too great. In this case a reasonable approximation to B(n, p) is given by the normal distribution
N(np, np(1 - p)),
and this basic approximation can be improved in a simple way by using a suitable continuity correction. The basic approximation generally improves as n increases (at least 20) and is better when p is not near to 0 or 1."
ok yeah I'm dumb but yeah this does show that we should be able to use CLT even for skewed distributions if we have a large enough sample (and generally I'd imagine poker samples are much larger than statistically large enough, which is typically something like 20 or 30).
Matt Vaughan
King of Moody Rants
Bronze Level
Yeah, don't feel dumb - duggs didn't get that it was binomial for ages
But yeah we can def use normality approximation, just keep in mind that we're talking about a simple binomial distribution, whereas in poker we aren't sitting there flipping a 70:30 coin and watching the outcomes. So we're prob getting something closer to a poisson binomial distribution (basically the sum of a bunch of binomial distributions with different success probabilities).
So yeh, in most cases I'd still say we could easily use a normal approximation, but we still need a bigger sample than we would for a single binomial distribution.
(http://en.wikipedia.org/wiki/Poisson_binomial_distribution)
hackmeplz
Sleep Faster
Silver Level
I mean the actual distribution can probably be figured out lots of 0.5 and 1bb losses and 1.5bb wins etc. But overall we can just use CLT to say that we can approximate it with normal distribution with winrate as mean and variance of our sample as the variance right?
Matt Vaughan
King of Moody Rants
Bronze Level
Yes, but that's not really what the initial point was discussing, which was more about all-in EV and how our win-rate is distributed around it.
If all we want to do is actually approximate the distribution of our winnings/hand outcomes, then yeah def look no further than sample win-rate and sample variance.
If all we want to do is actually approximate the distribution of our winnings/hand outcomes, then yeah def look no further than sample win-rate and sample variance.