Repping Strength Based on Stack Sizes

[Sherman]

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Edit: BTW, I made a post a long time ago about small sample sizes and stats. TBH, I think you are dead wrong if you say these sample sizes are too small to be useful. In the case of this hand, the BB is ~2.5 times more likely to have a true VPIP of 10 than of 20, ~7.5 times more likely to have a true VPIP of 10 than 30, and ~2.9 times more likely to have a true VPIP of 20 than 30. I'll try to search for and bump that old post.

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8 hands? Yes, I'd like to see your post -- I know many of the wonders of statistics, but 8 hands is less than 1 full orbit and definitely isn't enough to say with any great degree of certainty that BB is a nit -- the uncertainty of your assessment has to be pretty large. For example, I usually run 16/11 at full ring MTTs, but it's not uncommon to find stretches where I fold 20-30 hands in a row. Yes, you can tentatively say "he's most likely tight," but need to be cautious about making a close move that relies on him being extremely tight.

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Well, the search function on here sucks so I couldn't find the old thread. But I can re-post some specifics here.

The logic works as follows. If someone's "true VPIP" is .05, we know that the probability that he folds any given hand is .95.

So the math is quite simple. What is the probability of a person who folds 95% of the time, folding 2 times in a row? The answer is .95 * .95 = .90. That is, 90% of the time he folds twice in a row.

Now let us compare this person to someone who has a "true VPIP" of .10. This person has a .90 probability of folding and a .81 (.9 * .9) probability of folding twice in a row.

Given this, we can divide .90 by .81 to express the likelihood-ratio that a person is more likely to be a .05 than a .10 true VPIP given that he folded two hands in a row.

It works out that a person who folds two hands in a row is mathematically 1.11 times more likely to be a true .05 VPIP than a .10 VPIP.

Now that may not seem like much of a difference, but consider that we have gained this information off of only 2 hands! Beyond that, we also know that the difference between a true VPIP of .05 and .10 really isn't that different effectively. So let's compare a person with a true VPIP of .10 (very tight) to a person with a true VPIP of .30 (somewhat loose) after folding two hands in a row.

It turns out that a person who has folded 2 hands in a row is 1.84 times more likely to be a .10 true VPIP than a .30 VPIP. This same person is 3.6 times as likely to be a .10 true VPIP than a .50 VPIP!

All that information gleaned from only 2 hands! I think that is quite impressive.

In this case, we have a person who has folded 8 hands in a row. If his true VPIP is .10, he has a .43 probability of folding 8 hands in a row. Whereas if his true VPIP is .30, the probability of him folding 8 hands in a row is .058. That means it is nearly 7.5 times more likely that the BB in this hand has a true VPIP of .10 than .30! Pretty impressive IMO.

Now admittedly this analysis doesn't take account for position and many other things, but even if it improves your read on an opponent ever so slightly on average it is helpful. I wish I could find the original post. Maybe later today I will make a re-post that includes all of the analyses I have done on the topic.

Sherman