Zoltan on his internet machine

Maybe this is mentioned on the thread but are T-tests/CI a decent way to judge if you are a winning player despite a small sample size. Say you only have like 150 hours to play couldn't you still get a reasonable estimate of whether or not you are profitable by estimating standard deviation to do a T-test or CI

I vote phone for new forum mod!

GsentfrommykeyboardatworkG

Yes

When we make inferences about a sample to a population, we do something like this:

Randomly sample a bunch of people that represent the population.

When we do this we know each person is just as likely as another to be chosen (independence). Given that, if we do this process over and over the sample means are normally distributed (central limit theorem) regardless of the shape of the distribution, which is great.

What would this look like for a win-rate?

If we randomly sampled poker players across the world, we could get away with estimating the average person's win rate with barely violating assumptoins (win rates are not really independent of each other, e.g., if you play each other... probaly won't matter).

But what are we trying to do with one person's win rate? Make inferences about your general win rate from a limited number of session win-rates?

If so, we have problems. We might stretch ourselves and say that the win-rate from one session is a random sample of win-rates over all sessions if cards dealt were the only thing that mattered. Or that your tilt, skill level, etc. vary, but do so randomly That's probably not plausible.

But the sessions you make an inference from are definitely not independent. They come one after another and the results in one may affect the results in another (again, skill, tilt, etc.)

Furthermore, the population parameter you're trying to estimate (i.e., your "true" winrate) changes across sessions as your skill improves.

So, no, it doesn't really make sense to use a confidence interval and classic statistical assumptions.

A better approach is just to plot your win rates and watch them converge to a point. That will give you a better idea. If you really wanted to get fancy you could take a kind of Bayesian approach where you use one past win rate as an estimate of your win rate, then update your win-rate estimate given new evidence (new sessions). That's all too fancy. Just plot your win rates across each session in whatever metric you like and see how much variance/noise there is. That will give you a better idea of whether you are a winner.

Uhhhh... if you've played N hours, then say that you're testing for the win-rate over 1 hour with a sample size N?? Obv has some issues since individual values wouldn't be independent, but assuming you don't only play marathon sessions, I don't think it seems that bad.

I don't think that's any less reasonable than what you propose, and it's clearly more statistically rigorous, even if it has problems. Obv when your RV is changing over time, it's kind of sketchy to try to estimate the mean, but it's still better than nothing imo.

The general question (I think what the poster is after) -

is people hear:
"X hour sample is meaningless!"

... then they actually think independently and realize 'well, it can't be meaningless... but I wonder how much meaning it has..'

And I don't think any ponderer's concern is seven digit accuracy of confidence.. they just want to know if being up 2000 bb in 150 hours gives you 1% confidence in being a long term winner or 70% confidence in being a long term winner.

So in my opinion, who gives a **** if poker statistical modeling might get an F on a master's thesis - it still is practical and functional and better than saying "it is impossible to calculate". It is impossible to be perfect, but very possible to be close IMO.

At about that hour in my results, I calculated my percent chance of being a winning player through some likely hack method... It was over 90% - which allowed me to confidently take shots in higher games. I will try to find the post...

(Now having an actual distribution of win rates would be awesome - and help a ton with analysis - but that data collection will never happen)

I'm with you 100%. All models are wrong, but some are useful... as they say.

My point is that a Stats-101 confidence interval is not the best way to get a feel for how likely it is that your win-rate accurately reflects your ability. The problem with such a CI, which is really super super super easy to calculate, is that it is too precise and the assumptions beneath it are really problematic for thinking about a game like poker. The paradigm is just all wrong and it's wrong in ways that will give people the wrong idea about their game.

The problem with a confidence interval is tells us how often the constructed interval, based on our data, is likely to contain the true population parameter (our true win rate). The confidence is about the interval, not the estimate per se. We'd rather be able to talk about the confidence we have in our point estimate, not the interval around it. Bayesian statistics is the best way to arrive at such estimates.

Anyway I think all that's unnecessary here. My point is that someone, in my opinion, will get a better idea of the likelihood in there win rate by plotting their win rate over time and empirically looking at its shape and pragmatically assessing the data.

Some things we want to look at:

* Mean: average win rate, easy. But can be distorted.

* Median: I would contend a better estimate of your win rate. The nature of winning big pots or losing huge ones can result in some godly sessions and horrid sessions which may reflect random luck/bad luck more than skill. Median will ignore these.

* Standard deviation: this quantifies the spread of our win rate. If this is large, we should have less confidence that we are a winner, especially over smaller samples.

* Skewness: This is really, really important. There are ways to calculate skewness statistics, but the easiest way is to just make a histogram or kernel density plot of your win rates across sessions. If there are long tails on the negative side of winning, enough to seriously pull the mean towards these losses, we might learn something more important than "I am a winner or loser." We might learn: I am a winner in the vast majority of sessions but I have a huge tilt problem. Another easy way is just to compare your mean to median win rate. If they are substantially different in one way or another, that means you have large outliers skewing your data.

* Sample size: duh.

Of course, the prudent will realize the above are precisely what's necessary to calculate confidence intervals. But my point is that a confidence interval is much less helpful than actually plotting out your rates and analyzing it, and coming to a conclusion like:

"I'm mostly a winner: I've left a winner in 2/3 of the last 100 sessions. But I have the potential to tilt and really blow it: my mean win rate is substantially lower than my median rate, and it's costing me. On the other hand, I haven't booked nearly as many large wins -- I tend to win a lot and get overconfident and pick bad spots. My standard deviation is also quite large -- more than a buy-in at my game! That means the average difference between any one session's win rate and my mean rate is more than a buy-in. I am a high variance player."

That's a data-informed way of giving a player an idea about how good you may bb. It's far better than saying: My average win rate is X, with standard deviation Y, so assuming Z, 1.96xSD/sqrt(n) +- win rate = the boundary I expect my win rate to be.

A last point is that when we use inferential statistics like confidence intervals, we try to estimate a true parameter based upon a sample. Poker is weird in that we actually always have access to our true win rate, so long as we keep good records. We don't have to sample. We have complete data.

Our concern is our tendencies and the confidence that these rates accurately reflect a long-term trend. Diagnostic analysis of sample size, mean, median, standard deviation, skewness etc. will give us a much better analysis.

People can go ahead and construct a CI around a win-rate and say "I have 95% confidence that my true win rate lies in this interval." The thing is -- we don't need to guess at our true win rate. It changes over time and can be calculated. Instead we need to understand what's lurking underneath the summary statistic.

^ wow - awesome post

Thanks for the response and awesome post! I really appreciate the response I've been playing for about 4 months seriously, house games and such before that, so I'm trying to figure out if Poker is a viable way for me to help pay for school. I had never thought of making a scatter plot to look at skew I think I'll do that and good point about the win rate in relation to Confidence intervals

I'm gonna have to archive this one.

I'm still learning, too

I do quantitative social research for a living so this kind of analysis comes naturally... if only making tough decisions did in poker did.

Sent ise my DROID RAZR using 2+2 Forums[/QUOTE]

Learn how to quote and post much?

Ah, consistency:

Week 1 as 'pro:' -$200
Week 2 as 'pro:' +$2200

I found that ATM fees were really starting to get on my nerves and that I didn't really make that much interest at the bank. I don't really maintain a separate poker and life roll, so last October I took $5000 out of the bank to use as a sort of bankroll. If I play during the week I take 2 buy-ins and if I go on the weekend I take 3 buy-ins. Whatever I cash out that is not in hundreds I add to my wallet as walking around money (ie if I cash out $563, 500 goes to the bankroll and $63 goes to the wallet). Since October I have not gone to the ATM once and my bankroll is still over $5000. In addition I paid for Christmas last year in cash. This is a semi-brag post, but also an idea for people that are getting killed by ATM fees.

First month regularly playing 1/2 ever, and first month since black Friday playing poker on a regular basis at all. 13 sessions with an average length of 2.27 hours (I try to sneak in a few hours after work on the weekdays). 10 wins, 3 losses. Hours: 29.5. Winnings: $508. Hourly Rate $17.22. Not a bad supplemental income.

March: +$2500
April: -$1700

Yah $1/2 can be a real Mfer

$3/5 nl

March ~ 117 hours +$7506
April ~ 94 hours +$5

Rough April

What is the approach for winning a promo such as a high hand for x amount...do you count it to your win rate or not? Or just add it to the bankroll as rake back.

I include it as a separate game, so it shows in my overall results but doesn't skew my $1/2 hourly or my $2/5 hourly.

But there is a case to be made to simply include it as a normal session "win" since you're including all the extra jackpot drops in your results anyway.

Meh. Pick something that makes sense to you and stick with it.

I think short of hitting the bad beat jackpot when it's at some ungodly amount, you can include promos in your WR if you want - but don't feel obligated to. Like Angrist said, do whatever makes the most sense to you. If it's going into your bankroll then I would include it in my WR, personally.

i have separate columns for "gross" and "net" hourly on my excel. "gross hourly" includes everything including jackpots and promos while "net hourly" only pertains to the profits from the actual game.

Do you also change your hours based on time at the table vs time spent driving and on breaks?

no, i only count the hours i spent at the casino (including breaks). i kinda want to do apples to apples comparison to regular jobs so i don't count the time spent driving.

A question regarding stop losses and topping up at the table... Say for a 1/2 game, you bring 2 buy-ins, or $400. When is a good time to add on to your stack if you happen to take a hit early on?

I've had the problem where I top up like $30-40 and then get stacked. At that point I'm left with less than a full buy-in without going over the stop loss. Any tips on navigating these situations?