At what point does variance disappear?

[DavidC]

I understand that for any small amount of hands, there will be variance.

However, how many hands do you have to play before variance becomes a negligible factor in your results?

10,000 hands? 100,000? /images/graemlins/smile.gif

If anyone has some pointers as to how to find this out, please let me know, (even better if they know the answer).

I searched "variance" and it returned too many hits to be useful.

[caretaker1]

Variance will always be present, regardless of how long you play, it's inherent to the game. If your question is "How many hands do I have to play to be X% certain I'm a winning player?" Consult:

http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=838515&page=&view=&sb =5&o=&vc=1

http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=956937&page=&view=&sb =5&o=&vc=1

http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=854348&page=&view=&sb =5&o=&vc=1

[Kurn, son of Mogh]

Varience will never go away, but theoretically in the long run, the sum of positive and negative variance should approach zero. There is debate about what indeed constitutes the "long run". Since expert players do have losing years, I think you need to be in the 100,000 hand range to know for sure, but I may be being overly conservative.

The key is to examine and evaluate your play after every session. The first law of nature, after all, is "adapt or die."

[TMFS9]

I personally think that variance would never go away. The only way variance could ever go away would be to have your poker skills remain constant, and this would never happen. Because if you say that the variance will disappear after 100,000 hands, hopefully you will be a better player at hand #100,000 versus hand #1. There is also times that you begin to pick up bad habits, don't play for a while, have outside events affect your play (life), don't change with the times, etc. So to say that you average 2bb/100 hands over the last 100,000 hands would not be consistent with hands 100,001 to 200,000, because hopefully you will be a better player after the first 100,000 hands and your poker skills won't remain static.

[helpmeout]

I agree, variance isn't hugely important.

1. You play different opponents everytime you sit down.

2. Your read of the situation and or skills/abilities change all the time.

I think most semi-intelligent people should know how they are going after a certain amount of time. If you are winning in a session is it because you have had a good run of cards, your opponents suck or because you have been playing really well.

When you analyze your game you should know how good a player you are. Sometimes you will be getting bad cards for a few hours but only be down 10BB or so. Other times you will be getting good cards but only be up a small amount.

I know which situation I'd rather be in.

[DavidC]

Thank you very much for the responses, guys.

I appreciate the figure of 100,000, as well as the links, as well as the "adapt or die" sentiment, and the effects of improvement.

Most of this was stuff that I was aware of... I was kinda hoping for a mathematical explanation. The "x% certain" (statistically refered to as confidence level) is a step in the right direction. Basically, what I'd like to know is that I'm going to have (if I play statically) a 99.995% confidence level of getting a given result, if I play with the same people who play statically.

True, this isn't going to happen in real life, but this is the only way to isolate variance in such a manner as to analyse it in a meaningful manner. Otherwise you're stuck with "rule of thumb", which isn't horrible, but it's hardly something that you want to base your financial fate on, right?

I'll check out the other indicated forum posts, for sure.

Take care, guys.
--Dave.

[bisonbison]

Otherwise you're stuck with "rule of thumb", which isn't horrible, but it's hardly something that you want to base your financial fate on, right?

Well, even if you knew your win rate and SD with 100% confidence, you'd still be staking your fate on a wide range of potential outcomes over any finite number of hands. See Homer's Thread on Streaks (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=445039&page=&view=&sb=5&o =&fpart=1&vc=1) for an idea of how much your results can vary around your mean.

[Cosimo]

After 10,000 hands, a good player (2BB/100h or so) has finally played enough hands that any bad streaks should have been overcome, and he should be at least even. Full-time players (like David Ross) can play about 14,000 hands a week. Playing live, 10k hands means two months. Playing only at a weekend home game, it will take a year or two to get in ten thousand hands.

After 100,000 hands, a good player should have an accurate idea of his winrate. Seven weeks for the hardcore, and fifteen years for the dilettante.

After three months, a good online player is likely to be playing at different limits, and hence be in a completely different game. Maybe he'll try something different, too--like NL vs limit, tournaments vs cash games, stud or omaha vs holdem, or six-handed/HU vs full ring play. If he doesn't adapt, his EV is going to fall and his SD might increase.

After a year, the poker scene will be a different place. The WPT and ESPN's WSOP coverage changed the poker scene very dramatically. Is the current size of the player pool a fad, indicative of a culture that gambles more and will continue to do so, or a switch from slots, dice, and horses to cards?

Variance never disappears because you and the game will not hold still for long enough.

[DavidC]

Caretaker, that first post that you listed was absolutely perfect!

Thanks a lot,
Dave.