How long is long term???

[aclinml]

If playing a BJ game with a .5% advantage for the house, how many hands does it take to get the 'long term' results very close to the .5% EV?

 

[Mikeaber]

If playing a BJ game with a .5% advantage for the house, how many hands does it take to get the 'long term' results very close to the .5% EV?

I don't think you can really quantify "long term". It's a mathematical concept used to express more or less as an average, what a projected computation of probability will be. The more hands you play, the more likely you are to approach the projection. But to say 10,000 hands would be no more accurate than to say 100 hands....you'd just have better odds in matching the projection with 10,000 hands...or better yet, 1,000,000 hands!

 

[aclinml]

I guess my question should be, how many hands played are needed to have a 95% chance of being within 10% of the EV?

 

[Mikeaber]

I'll leave this one for ZG or Ken. I do not know how to put a number down as an answer. But, if you are trying to say that in the "short term" you could do better by deviating from Basic Strategy or playing progressions, you would be making an invalid leap of faith. Short Term or Long Term, playing with correct strategy is always correct.

 

[Sonny]

A few assumptions here:

Average bet = 2.5 units
100 hands per hour
Win rate = 1.25 units per hour
Hourly SD = 26 units

You have a 68% chance of reaching your EV after 43,264 hands (about 433 hours). You have a 93% chance after 173,056 hands (about 1,731 hours) and a 97% chance after 389,376 hands (3,894 hours).

With such a small EV and large SD it will take a loooong time to approach the long run. It will also take a huuuuge bankroll to preserve a reasonable ROR.

-Sonny-