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Originally Posted by MeleaB
Where does your current understanding come from? It's not from playing the games and it doesn't appear to be based on any evidence. As posted above, results from a variance simulator will probably surprise you.
I know you think that I don't know what I'm talking about, but probably unknown to you is that I've been writing about this stuff for over 30 years. This goes back to my book
Gambling Theory and Other Topics which was first published in 1987 and to some articles which I wrote the previous year. So let's look at this from that perspective.
In the example above we have a win rate of -20BB per 100 hands and a standard deviation of 100 BB per 100 hands. So first let's convert this to an hour of live play. (This needs to be done since the relationship of the win rate to standard deviation is not linear).
First, 100 hands is about three hours of live play. So dividing -20 BB by 3 produces a win rate of -6.67 BB per hour of live play. The standard deviation now needs to be divided by the square root of 3 which is 1.73 producing a per hour standard deviation of 57.8.
Now going back to my book, on page 90 and 91, where "The Ideal Game" is addressed, I noticed that when this ratio of the win rate divided by the standard deviation (for one hour of play which is why I made the conversion) was about 10 percent things will be as we want them to be, and I wrote:
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I believe this enables the expert to win fairly consistently but still allows enough fluctuations to keep weak players hooked.
Now while not specifically addressed, I think it's fair to say that if this same ratio for the recreational player is approximately -10 percent, that's what we also want. That is the recreational player will now experience enough fluctuations that he'll have enough winning sessions to keep coming back even though his overall expectation will be negative.
Now in the example given. if we take the win rate of -6.67 BB and divide it by 57.8 BB we get 11.5 percent, which is fairly close to my ideal 10 percent. So this says to me that if this example is reasonable, the games on the Internet should not be contracting in the way that they are.
When I did this work in the past, I collected a fair amount of data from my own play and that of a friend. At the time, we both played limit hold 'em and seven-card stud (no-limit hold 'em games were not available and Internet poker did not yet exist) and this is why I'm confident in these numbers. But I don't have the same type of information/data for no-limit games on the Internet and certainly don't have a good estimate for the standard deviation of a recreational player on the Internet.
But logically I think there is something we can assume and it has to do with what the standard deviation is for the recreational player. Specifically, if he's playing in a game where most of the other players are multitabling, it's probably correct to assume that these other players are playing quite tight. And when that's the case, this should be reflected in the standard deviation for the recreational player. That is, it would be lower, and perhaps much lower, than what you would expect from this same player if he was in a game that consisted mostly of strong players who were only playing one game. That's because these players would now be playing more hands and making more plays such as thin value bets and semi-bluffs that would drive the standard deviation of their opponents, including the recreational player, up.
So I question as to how good the estimate of 100 big blinds per 100 hands is for the recreational player. If this is a good estimate, then there almost has to be a different set of reasons as to why the games are contracting. If it's not a good estimate and a much lower standard deviation is accurate, then this is the most likely answer.
Mason