You're sample size is too small.

[BeerMoney]

I've had a coupla thoughts about that phrase that is commonly thrown around around these parts.

If I set up a hypothesis of

Ho: player is a break even player or worse Vs.
Ha: Player is a winning player

And i have that player play 3 STT's and he get's 2 firsts, and one second, we could compute a p-value for that player, and that p-value would be rather small, and the evidence would lead us to believe the player is in fact, a winning player. There is nothing wrong with this experiment, statistics apply to poker the way they do to everything else. And this comes from a sample size of 3.

Now, a poster comes on and says for my first 50k hands I was +4BB/100 now for my last 50k i was break even!! What gives?? And a bunch of people come on here and say that you need a sample size of approximately 55 Billion hands to estimate your true win rate. I would argue that over those first 50k his true win rate was near 4 BB/100 and over his last 50k, his true win rate was near 0 BB/100. Why??

I believe the games change. Old opponents get tougher, more educated, more aware of your style. Perhaps over this last 50k the economy sucked, and fewer new players were coming on to party. This player may have done well to keep their head above water. Throw in some tilt due to frustration, and no wonder things seem so bad. Games as a whole may cycle from slight more agressive to more passive... tight to loose, etc.. All of this means that your true win rate is in fact a random variable also. Today, you may be a 4 bb/100 winner, but we don't know what will happen next month. Maybe the story of Jeff Madsen will bring out even more fish. Who knows.

Bottom line, qualitative evaluation is better than anything. Stellarwind said it a while back, and i still agree with it.

[SamIAm]

I think your tilt and your opponents changing over time and so forth is MUCH less important than whether you flushdraws hit.

Luck >> Skill in the short term. Short term = 54.9 billion hands.
-Sam

[WhiteWolf]

Beer Money -

These two statements are not contradictory:

1) Game conditions + a player's skill level will change over 100 K hands
2) 50K is not enough hands to give you a strong confidence level in your win rate.

[Nilzor]

I've made the same thoughts as OP, and I think he has a valid point.

What you're saying is basically that there's minimal skill involved in poker. If luck >> Skill over 54 billion hands, luck >>>>>>>>>>>>&g t;>>>>>>>>>> skill over 50k hands, right?

I call BS

[SamIAm]

I would hope you recognized that the precision in my "54.9 billion" was tongue in cheek. It's just under the number used in the OP.

If you want to replace "54.9 billion" with "surprisingly many", that's cool.
-Sam

P.S. It's awesome that this is your 6th post in 2 years.

[jtr]

BeerMoney, you know what a confidence interval is right? I promise you that a typical NL player over two different 50,000 hand stretches, even if they played the same way and the game conditions didn't change, could expect the win-rates for those two stretches to differ by as much as 4PTBB/100 easily.

The rest of what you said I'm not going to argue with, but rest assured that 50,000 hands really isn't a good enough sample for being confident in your win-rate to the nearest integer.

[Nilzor]

Ok well I still disagree with you. 50-100k hands is a fair number to estimate your winrate. And if your opponents change during that period of time or if you go on tilt half of the time, my assertion is that your winrate WILL be affected more than luck will compensate for.

But of course I cannot prove that, and you cannot prove your claim so I guess there's no point discussing this further.

P.S. Thanks, I guess you say that to discredit my post. Yet my post count says nothing about how much I know about poker.

[jtr]

[ QUOTE ]
Ok well I still disagree with you. 50-100k hands is a fair number to estimate your winrate. And if your opponents change during that period of time or if you go on tilt half of the time, my assertion is that your winrate WILL be affected more than luck will compensate for.

But of course I cannot prove that, and you cannot prove your claim so I guess there's no point discussing this further.

[/ QUOTE ]

Nilzor, I only half want to argue with you here. Obviously you're correct that bad play and a changing cast of opponents will influence your winrate over 50K or 10K stretch of hands. But you seem eager to suggest that luck can't play much of a role in winrate over those sort of hand numbers. This just isn't true, and we can prove it.

Take a typical small-stakes NL player, winning at 5PTBB/100. His standard deviation will probably be something like 35PTBB/100. Maybe higher or lower depending on his style, but that's a good initial estimate. So over 100,000 hands, the 95% confidence interval for this guy's winrate is between 2.83 and 7.17 PTBB/100. Now this means that if he plays 100,000 hands one month and wins at 2.83, and he plays 100,000 hands the next month and wins at 7.17, it might be because he improved or his opponents got worse or whatever, but we don't actually need to invoke a hypothesis like that, it could simply be that he had a good run of cards or a bad run of cards. That's what a confidence interval means; it's a way of getting a handle on how much variance can affect your results.

To get to a point where your argument works, and the guy can't appeal to bad luck or good luck to explain his winrate, we need to work with much larger samples of hands. To get the confidence interval down to +/- 0.5 PTBB/100, for example, would require about 1.8 million hands.

[SamIAm]

[ QUOTE ]
P.S. Thanks, I guess you say that to discredit my post. Yet my post count says nothing about how much I know about poker.

[/ QUOTE ]
I'm sorry, I really didn't mean it to discredit your post. WRITING about poker doesn't make one smarter. Maybe reading does, and you've clearly been doing that as long as everybody else in this thread.

I seriously just thought it was interesting. Sorry to offend.
-Sam