Probability of win rate given 5% sample

[Mark1808]

A player posts a 6 Poker Tracker BB win rate per 100 hands over 150,000 hands. I have 8,800 hands on him at 1/2 Poker Tracker BB per 100 hands. Lets supppose the Standard Deviation per 100 hands is 35 PTBB per 100 hands. What is the probability of a random sample of 8,800 hands being 1/2 PTBB per 100 hands win rate given a 6 PTBB per 100 win rate over 150,000 hands?

[pzhon]

[ QUOTE ]
A player posts a 6 Poker Tracker BB win rate per 100 hands over 150,000 hands. I have 8,800 hands on him at 1/2 Poker Tracker BB per 100 hands. Lets supppose the Standard Deviation per 100 hands is 35 PTBB per 100 hands. What is the probability of a random sample of 8,800 hands being 1/2 PTBB per 100 hands win rate given a 6 PTBB per 100 win rate over 150,000 hands?

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After 8800 hands, the standard error is 35 / sqrt(88) ~ 3.73

If we observe a win rate of 6.0 PTBB/100 over 150k hands, the true win rate is not necessarily 6 PTBB/100, but let's assume it is for this calculation. 0.5 PTBB/100 is 5.5 PTBB/100 below average, or 5.5/3.73 ~ 1.5 standard deviations below average. A result that extreme or more in that direction will happen about 7% of the time.

By the way, if you were playing at the table rather than just observing, then your presence biases your observations, presumably dropping the observed win rate by 1-3 PTBB/100.

[Mark1808]

[ QUOTE ]
[ QUOTE ]
A player posts a 6 Poker Tracker BB win rate per 100 hands over 150,000 hands. I have 8,800 hands on him at 1/2 Poker Tracker BB per 100 hands. Lets supppose the Standard Deviation per 100 hands is 35 PTBB per 100 hands. What is the probability of a random sample of 8,800 hands being 1/2 PTBB per 100 hands win rate given a 6 PTBB per 100 win rate over 150,000 hands?

[/ QUOTE ]
After 8800 hands, the standard error is 35 / sqrt(88) ~ 3.73

If we observe a win rate of 6.0 PTBB/100 over 150k hands, the true win rate is not necessarily 6 PTBB/100, but let's assume it is for this calculation. 0.5 PTBB/100 is 5.5 PTBB/100 below average, or 5.5/3.73 ~ 1.5 standard deviations below average. A result that extreme or more in that direction will happen about 7% of the time.

By the way, if you were playing at the table rather than just observing, then your presence biases your observations, presumably dropping the observed win rate by 1-3 PTBB/100.

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Thank you very much. Why does my presence effect the win rate and why does it effect it negatively?

[pzhon]

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Why does my presence effect the win rate and why does it effect it negatively?

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If you are a breakeven player or a winning player, then you are absorbing a signficant amount of the dead money when you are playing at the table, rather than contributing dead money as a typical losing player does.

It would be more obvious if the table were heads-up. It's quite reasonable for a heads-up player to win on average, but not against you, or not as much against you.