On Imperfect Imperfection: A Theory Post (Mad Long Yo)

[yegon]

[ QUOTE ]
First off lemme say good post and thank you for trying to explain this. I have a question though. You made this post mainly about the other post which you linked. In that post,the villain only had about 33 bb's I think. That of course left us as hero, in a push or fold situation. How much does all of this change if villain had 100 bb's or 200 bb's?

[/ QUOTE ]

I do not think this concept affects us much in the hand that was mentioned if we would be deeper. We would have to fold the same no matter if we had 25% or 35% equity. We have no draw and are OOP and would likely face bets on later streets.

[Profish2285]

So if we are any deeper than what we are, then this becomes a clear fold youre saying?

[Gelford]

Grunch

So the cliff notes of this post are as follows?


You assign a range, then you estimate a surrounding margin of error. Depending on the volume of this margin on both sides of your assigned range you get a generel direction of which way to adjust (or which directions are costly to err in and which are not on the loose-tight scale)


Nothing earthshattering if I understand you right, but might be a usefull tool.

[yegon]

yes it is a fold

the difference is the threat of other bets from villain. Even if we are ahead we would have to check the turn showing weakness and we might get pushed off the hand by worse.

[Antinome]

When you have an abnormally tight player over a small sample some regression to the mean is likely to occur and this should be taken into account in range assignment.

You could call it an application of Bayesian decision making- given the prior knowledge of the actual distribution of tight players, the probability that he he is tighter than he appears is small and the probability that he is looser is large.

The observation seems valid. Quantify it. [img]/images/graemlins/smile.gif[/img]

[bozzer]

[ QUOTE ]
When you have an abnormally tight player over a small sample some regression to the mean is likely to occur and this should be taken into account in range assignment.

You could call it an application of Bayesian decision making- given the prior knowledge of the actual distribution of tight players, the probability that he he is tighter than he appears is small and the probability that he is looser is large.


[/ QUOTE ]


yep exactly. OP is on the money IMO. when we see weird stats in small samples we have to remember that it is likely that these players are not truely as weird as they appear from a small sample, and we should skew our ranges slightly more in the direction of them being an average player. this might appear to contradict a post i made a while ago, but i still think some stats have more validity in a small sample than people realise.

AF on the other hand seems to require a big sample, so is particularly appropriate for OP to comment on.

if someone statistical wants an idea for a great theory post, run some analysis on the common stats like vpip/pfr/af/wtsd etc and give us the confidence intervals for these at different values and sample sizes. it would be so useful!

for people who like graphs, here's a graph i made earlier summarising OP's point: