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Poker News | Online Poker | News

If You’re the Favorite, Should You Leave?

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Most of our modern Geometry is based on Euclid's Theorem, "Through a point outside a line, there is one and only one parallel line." The problem is that it could never be proven. In fact an attempt to prove it by proving that the alternative was un-true not only failed, but resulted in a whole new Geometry. Non Euclidean Geometry is the basis for most of our super-advanced mathematics like Quantum Mechanics and String Theory today. Maybe a better analogy would be: Theoretically a bumble bee can't fly but empirical evidence seems to suggest otherwise. As most of you have probably guessed I'm about to suggest something that isn't part of Poker theory and in many cases maybe the biggest sacrilege in Pokerdom.

Common wisdom, Poker Dogma and all the poker "authorities," decry walking at a predetermined "win" point as ludicrous and foolish. If the game is good and you are the favorite, you should remain in the game. The poker player is paid at his hourly win rate and should continue to play as long as he is the favorite. By leaving at a predetermined "win" point, you limit your winnings not your losses. Play as long as the game is good.

Well I understand the reasoning and agree, but I do believe that the empirical evidence in this case may suggest another approach. Over the long run "luck" evens out and everyone will eventually get their share of cards. If they maximize their wins with good cards and minimize their losses with marginal cards, they will be "winners" over the long run. The problem is that the long run is divided into weeks, days, and sessions. And over that short period of time the cards often do not even out. In fact they tend to clump together in groups. Luck or short term variance may not matter in the long run, but it does matter in the short term and determines if you walk a winner today.
Let's look at an example. (For those of you who work with Wilson's Turbo Texas Hold ‘em, this is the Maverick profile.) Here is a graph of twenty 300 hand sessions and the expectation based on one million hands.

The red is the expectation based on one million hands. It continues to grow. The yellow is the change in total bankroll at the end of each session. The pink is the highest win point during the session and the purple is the lowest point during the session. The light blue is based on a stop win/loss point of one average variance. In this case $500 and an average win rate of $128 for the series of sessions. So if he won $628 stopped. If he lost $372 stopped. If at any time he had a swing of 500 one way or the other stopped. As you can see by the blue line a stop W/L point would have improved the player's results over this rather bad streak of cards. I've conducted a dozen of these simulations so far and all indicate there might be a value to establishing a stop point.

Let's make an assumption. If you could quit at 90% of your biggest stack during each session, wouldn't your hourly "win rate" increase? The problem is how we calculate this target value. Like most players you should keep good records of all your sessions. You should be able to calculate your win rate and your variance. Usually we use the big bet as the measure of success, like three big bets per hour for a win rate. I've found that when making expectation calculations the average pot size is a better indication of the expectation than the Limits. Every poker player knows that their expectation in all $5-10 games is not equal, but in terms of the average pot size they can be compared more accurately.

So, could we improve our win rate if we could establish a viable stop win point and a good stop loss point? Definitely the problem is the calculation for these two points. In statistics, 95% of all results occur within 2 standard deviations of the mean. Shouldn't there be a way to calculate this value and establish meaningful stop points?

Good Luck - jb

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