so How Long IS the Longrun? *4 questions*

[jono]

[ QUOTE ]
The long run is a very long time. Mathematically it's a limit. It approaches infinity, it's an arbitrarily long period of time. Pick a length of time. Any length. The long run is longer than that.

The long run is in fact forever. It's an infinite length of time. You never get there, you just get closer and closer. And, things don't even out. They average out.

[/ QUOTE ]

*comments on this?

*for an aggressive short hand game how long is effectively the long run?

*in this same kind of game, spurts of how many hands could a winning player effectively run bad for AND still be negative?

*for a 125,000 hand sample, could a true winrate 2BB/100 player run at 1BB/100 due to luck? Could a 3BB/100 run at 1BB/100?

[Phil153]

This can be answered, but it varies by style and game type. What you can get is a "confidence interval" where you're 95 or 99% sure your true winrate falls in a certain range.

To calculate this you'd need to know a typical standard deviation for aggressive, short handed games. You can get this in PokerTracker by clicking "more detail" on the session notes tab. The value will be in BB/100.

Once you have this, you can calculate the 95% confidence interval around your winrate like this:

true winrate = reported winrate ± 1.96 * standard_deviation/sqrt(hands/100)

For example, if you'd played 125,000 hands with a winrate of 1BB/100 and a standard deviation of 20BB/100, your true winrate would fall into the range

1BB/100 ± 1.96 * 20BB/100 / sqrt(1250)

= 1BB/100 ± 1.11BB/100

So if you're getting 1BB/100 over 125K, your true winrate is between -0.11BB/100 and 2.11BB/100 95% of the time.

Note this is just an example; you'd need the actual value for the standard deviation for your game type. My standard deviation is 105BB/100, yours may be as little as 15. The smaller the standard deviation, the quicker results converge.

[6471849653]

[ QUOTE ]
1BB/100 ± 1.96 * 20BB/100 / sqrt(1250)

= 1BB/100 ± 1.11BB/100

So if you're getting 1BB/100 over 125K, your true winrate is between -0.11BB/100 and 2.11BB/100 95% of the time.


[/ QUOTE ]

Only when the balance of good and bad luck has been achieved during a long run like 100 or 200K of hands the simple formulas can tell what happens during the next 100 or 200K of hands. That is the additional formula (the simple formulas give some e.g. 5% or less happening after some point, but it's not true), and it's difficult when it comes to poker also because the bad runs happen more rarely (but are extreme); it takes still a longer time before the simple formulas hit in as accurate.

At 5K of hands they have no accuracy, at 10K they can't be trusted one bit (other than indicating that one may be a winning player), but they can be trusted somewhat with 2bb/100 (but not with 1bb/100) when at 30K of hands, and at 100K one can practically trust them totally, though not yet with 1bb/100 that may need 1000K of hands to get to that same trust point.