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#1
04-17-2007, 10:35 AM
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A Note on Variance
People always talk about running bad, getting coolered then going busto on these forums. In short, I tested the veracity of these claims. The following chart show about 31k hands where a 30 Heros have committed exactly 1/20th of their bankroll in pots they are either a favorite or an underdog. The average P (hero is a favorite in 1 hand) is 50.02%. This equates to a “2% edge” or 2bb/100. However, since Heros cannot always be exactly a 50.02% favorite in each individual hand, I’ve randomized Hero equity for each hand into 10 common equity buckets. When Hero’s are ahead, they are: 80%, 75%, 60%, 55%, or 66% favorites. When behind, they have equity inverse to that above. Heros are more likely to be slim favorites than huge ones (ie, you’ll have 1 over card vs. villain more frequently than an over pair). The pool of random equity must therefore adjust for commonness of situations AND Hero edge. To do this, I used excel to select random equity from a column of over 2.2k rows. The frequency (as % of possible equity situations) of being a favorite 2%, 20%, 50%, 1.25% and 30% when Hero has equity of 80%, 75%, 60%, 55%, or 66%, respectively. In other words, 50% of the time hero has positive equity, he will be a 60/40 favorite. I’ve upward adjusted the positive equity frequency to account for a 2% edge. So the average equity of the sample is 50.02%. The graph is the cumulative log returns on an original bankroll.
 As you can see, 2 of 30 will be superstar robustos (up more than 3000%) in practically no time and 5 will go busto. Since in practice Heros almost always have less than 1/20th of their roll at risk when they play a pot (usually pots are 15bbs not 100), the variance and results of this chart could take 8x-10x as many hands to be realized. Yet, I believe it is a reflection of pokers true variance. Comments and critiques are welcome. Trolling is not. GL at the tables. 
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#2
04-17-2007, 03:10 PM
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Re: A Note on Variance
what
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#4
04-17-2007, 03:59 PM
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Re: A Note on Variance
They don't lie, at least not all the time. Selective memory is to blame, I would think. If you get all your money in with the best hand you are going to have an upswing more than 50% of the time HU. Except for the two spikes that shot up really fast and a couple that got in the red after a couple thousand hands, I don't see anything necessarily surprising here. Just a steady increase for the hero. The thing is they remember their bad beats more often than their wins, so it's more about posting and accentuating the positive things about your game. If you say "some donk felted me on pokerstars the other day" or "fish hit a two-outer on me last night" people are just going to think you are, in general, a losing player, even if you aren't.
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#7
04-17-2007, 04:56 PM
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Re: A Note on Variance
No, I did it because I wanted to know what kind of variance a winning player can reasonably expect to have. While the graph isn't in color, I'll note the biggest swing you can have here is 10.5 BI.
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#8
04-17-2007, 05:14 PM
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Re: A Note on Variance
10.5 BI in 30k hands...bump it to 100k main
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#9
04-17-2007, 05:27 PM
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Re: A Note on Variance
Since you don't risk 1/20th of your bankroll every time you risk money, you should use average $ risked and adjust for # of hands you play relative to number of hands dealt. If the average pot = 15bb, then realistically you are risking 100BB/15BB =~ 7. Now if you play 30% of your hands (6max), gross that 7 up to 7/.30 = 23. Essentially the hands in the graph represents situations where money is risked. Multiply hands by a factor of 23. 23 x 31k = 713k. This is why you don't really need 200k hands to know if you're a winner. You need like 9k-10k situations where you make decisions.
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