This post is based on some thoughts I had around how fast I could reasonably grow my bankroll. Some basic assumptions:
1) You are comfortable at playing at a limit where you have 300 BB (Big Bets). Where this number comes from and how to derive your own “comfortable” bankroll size will be a topic for a future blog post.
2) You are a good player in the games and limits you choose.
3) You see 60 hands per hour per table.
Given these assumptions, you can make some rough time estimates around your bankroll progression – specifically, how long it will take to double your bankroll to allow you to move up to the next level if you desire.
A standard metric for the rate at which a good player can beat a game is for 2 Big Bets per 100 hands (2 BB/100). To double your bankroll requires you to earn another 300 BB. At the "standard" rate, this should take you 15000 hands (300 BB needed @ 2 BB/100) or 250 table-hours.
So, how long should it take you to put in 250 table-hours? That obviously depends on how much you play and how many tables you play:
These timeframes are very short, especially when a typical “double your money” timeframe in the stock market is measured in multiple years. WOOO HOOOOOOO – let’s quit my job, cash in the retirement account, mortgage the house, and play poker – I’ll be a millionaire in no time!!!!
Except for one thing: variance - the variance around this 2BB/100 earn rate is extraordinarily large, and we can actually estimate how large via basic statistical methods. For instance, take a hypothetical player with a 2 BB/100 win rate, with a standard deviation of 16 BB/100 (which is actually a little low by some measures. Let’s say this player plays a low-variance strategy). Let’s say you clone 10000 identical copies of this player and send them all out to play 15000 hands. As a group, they would average a 300 BB win. But the individual breakdown of the population would be something like the following (from a basic simulation done in Excel):
10 people would be down more than 300 BB (and thus be broke!)
102 people would be down 150-300 BB (and may have dipped below 300 BB in the process)
524 people would be down 0-150 BB
1560 people would be up 0-150 BB
2843 people would be up 150-300 BB
2767 people would be up 300-450 BB
1585 people would be up 450-600 BB
493 people would be up 600-750 BB
102 people would be up 750-900 BB
14 people would be up more than 900 BB
When graphed, the shape of this is a classic “bell curve”
Thus after 15000 hands a total of almost 6.4% of the players would be losing (instead of up their “expected” 300 BB profit) and over 2% of the unlucky souls will be down over 100 BB! That is a huge variation, and is solely attributable to randomness – remember, these are all clones of the same player with the same win rate and standard deviation! Also remember that these are good players, playing a low variation strategy!
So if 6% of the players are losing over a span of 15000 hands, then that really implies 15000 hands is not enough to truly determine who is profitable or not. Let’s ask some more questions:
- How many hands does this group have to play before (say) 99% of the population will at least be positive? Via the same simulation, this number is somewhere is the neighborhood of 33000 hands – which will take you about twice as long as the number in the table above.
- How long do they have to play before 99% of them get to their “expected” 300 BB profit? Via the same simulation, somewhere around 60000 hands, or 4 times the amount of time as in the table above.
OK, great! So even if it takes me 32-48 weeks to double my bankroll (instead of the original 8-12 weeks, before we included variance), that’s still better than waiting years in the stock market!
However, let’s think about that last bullet for a bit. As stated, after 60000 hands, 99% of the population would be at 300 BB or better. Great. But let’s look at what the clones would calculate for their own individual winrates: the very lower end of that spectrum would think they were 0.5 BB/100 players (300 BB / 60000 * 100), and (since the distribution is symmetrical) the upper end would think that they were 3.5 BB/100 players. This is from a group of identical 2 BB/100 players! Even after 60000 hands, the calculated winrates can be far, far off the actual winrates solely due to variance. To be fair, about 70% of that population would calculate their winrate to be between 1.3 BB/100 and 2.7 BB/100, but that is still quite a wide variation!
The point is that you really have no way to determine that you are a 2 BB/100 player without playing an incredible amount of hands – your at-any-given-point-in-time current calculated BB/100 rate is pretty much worthless without tens of thousands of hands behind it, and who knows if you’re even playing at the same winrate as you were when you started the series of hands? Hopefully you’re getting better over time……
Is there a lesson here? It certainly isn't "don't bother to calculate your BB/100, because it can't ever be pinned down." You have to have some number to gauge your ability, and even if it comes with large "error bars" it is better than nothing. Perhaps the lesson is to not make any long-term plans based on whatever your current BB/100 is - that if you play a lot of hands, play them well, and accept variance as part of the game, that bankroll considerations will take care of themselves. This is easier said than done, as both poker1eh and myself have learned in our very short stint into this silly game.
My next post will likely be math as well - about bonuses and bonus chasing, and what they can do to modify the figures above.
No comments:
Post a Comment