welcome to the rock.

[Aaron W.]

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But this guy's numbers suggest that he doesn't raise AK here; even if we assume a decent deviation of like 3% true pfr AKs basically isn't in his hand range. Plus these super-tp types are usually more inclined to raise with big pairs than big overs regardless of if they're in the top x% of hands.

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1% PFR is about 13.25 hands (1326 total starting hands). There are 6 pocket aces and 6 6 pocket kings. That makes up most of the 1%. If you give the HUD a 3% error, he could be raising as many as about 53 hands, and you'll have a tough time reaching that number without including AK. In fact, you'll have a tough time getting up to 2% (given that you have JJ) without getting some AK hands thrown in.

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I'm not sure that suggesting a 3% margin of error is appropriate. This is a statistical question: What is the likelyhood of this sample being representative of the entire data set. It is quite possible that his best hand in this data set, the one that he decided to raise with was AJo. More accurately, we need a figure like: what is the probability of having AA-QQ not present in random sample of 150 hands. This should help us decide to make the call. I'm chintzing out on math again, because it's 5 p.m...time to go home.

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I'm not a statistician, but here's something to consider: In political polls, a sample size of 1500 or so ends up with an error around 3%. Our sample size is much smaller than 1500.

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But this guy's numbers suggest that he doesn't raise AK here; even if we assume a decent deviation of like 3% true pfr AKs basically isn't in his hand range. Plus these super-tp types are usually more inclined to raise with big pairs than big overs regardless of if they're in the top x% of hands.

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1% PFR is about 13.25 hands (1326 total starting hands). There are 6 pocket aces and 6 6 pocket kings. That makes up most of the 1%. If you give the HUD a 3% error, he could be raising as many as about 53 hands, and you'll have a tough time reaching that number without including AK. In fact, you'll have a tough time getting up to 2% (given that you have JJ) without getting some AK hands thrown in.

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I'm not sure that suggesting a 3% margin of error is appropriate. This is a statistical question: What is the likelyhood of this sample being representative of the entire data set. It is quite possible that his best hand in this data set, the one that he decided to raise with was AJo. More accurately, we need a figure like: what is the probability of having AA-QQ not present in random sample of 150 hands. This should help us decide to make the call. I'm chintzing out on math again, because it's 5 p.m...time to go home.

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I'm not a statistician, but here's something to consider: In political polls, a sample size of 1500 or so ends up with an error around 3%. Our sample size is much smaller than 1500.

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Our sample is ~10% of the entire set, which is fairly representative. A political poll of 1500 may be more like <1% of the entire sample.

I fold. I feel there is no way he has any card below a jack.

[Redd]

The 3% error of margin is my fault; I just picked an arbitary number (I was actually referring to a 2% margin, for a total 3% true pfr). But as Aaron pointed out my combinatrix were all wrong for that post anyways.

Aaron, you're completely right that if Villain has been running very cold for 150 hands that AKo/s is a possibility. Regardless, I still don't see how you're raising for value. If we assume Villain's range will include any AK combo, suited or unsuited, without being discounted, our equity is around 30%:

Text results appended to pokerstove.txt

19,870,449,984 games 150.337 secs 132,172,718 games/sec

Board:
Dead:

equity (%) win (%) / tie (%)

Hand 1: 30.2506 % [ 00.30 00.00 ] { JJ }
Hand 2: 53.9030 % [ 00.54 00.00 ] { AA-JJ, AKs, AKo }
Hand 3: 15.8463 % [ 00.16 00.00 ] { random }

We go to around 23% if he'll only raise AKs from this position. Of course, the limper will likely have a better than random hand as well.

So we'll probably be able to cold-call profitably if he'll include all of the AK offsuits. It's hard to predict what will happen behind us and postflop but equitywise, it looks like close call between cc/fold if he'll only raise AKs here. Anybody know how we can we estimate the standard deviation in his pfr after n hands?

Unless he's raising more than this hand range, I can't see how we get value out of a 3-bet.

[robertsonjohn]

If you really believe your stats, logic says you should probably fold, but emotion, boredom and statistical margin of era may lead you to act otherwise.

As a meaningless aside, if you decide to call/3bet, and he leads out on a AKJ flop, what's your play?

[Aaron W.]

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I'm not a statistician, but here's something to consider: In political polls, a sample size of 1500 or so ends up with an error around 3%. Our sample size is much smaller than 1500.

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Our sample is ~10% of the entire set, which is fairly representative. A political poll of 1500 may be more like <1% of the entire sample.

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It's the sample size that matters, not the total number of possible hands.

Here's a thought experiment that should convince you this is true. Suppose you have a bucket of 10 balls, 5 black and 5 white. When you draw from the bucket, there's a 50% chance you will draw white. Every time you draw a ball, you put it back in the bucket. You do this 100 times. You will expect to have about 50 of each color drawn.

Now you repeat the experiment, but with a bucket containing 10 billion balls, 5 billion of each color. Each draw still has a 50% chance of being white. If you do this 100 times, you will expect to have about 50 of each color drawn.

The only factor that matters is the distribution, not the total number of balls in the bucket.

[Redd]

This isn't a fair comparison to the poll example. In the little bucket you're testing 1000% of the sample size. If you drew 1000% of the sample size from the big bucket (ie, 100 billion balls), you'd get a much closer %white to the true 50% probability.

Obviously if we poll 99% of the population we'll get a more accurate response than polling 1% of the population, regardless of population size.

But I don't mean to derail the thread - does anyone have a simple estimate of the deviation of pfr? If the Villain in the OP was 1% pfr over 1000 hands, it's a standard fold. If over 20 hands, it's a standard 3-bet. So the questions become:
1) At what number of hands does our read have to be over to justify a pf-fold? It's obviously somewhere between zero and 1000.
1) At what number of hands does our read have to be over to justify a cold-call (if any?)

[Aaron W.]

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This isn't a fair comparison to the poll example. In the little bucket you're testing 1000% of the sample size. If you drew 1000% of the sample size from the big bucket (ie, 100 billion balls), you'd get a much closer %white to the true 50% probability.

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But each sample is statistically independent. It makes no sense to say you're testing larger than the size of the bucket. The only factor that matters is the number of draws because of the independence. This is the whole point! You can tell that the balls are distributed roughly 50-50 by taking 100 samples from a bucket with 10 balls and a bucket with 10 billion balls.

Here's another example. Imagine flipping one coin 100 times. You expect there to be about 50-50 split between heads and tails. Now flip 100 coins all at once. You've taken one sample of 100 coins instead of 100 samples of one coin. Do you expect there to be much difference? In the first case (by your terminology), you've sampled 50 times the sample size. In the second case, you've sampled 2^{-100} of the sample size. Do you expect any difference?

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Obviously if we poll 99% of the population we'll get a more accurate response than polling 1% of the population, regardless of population size.

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This is the error. When you say "poll 99% of the population", you're assuming you never ask the same person twice. This means that your second sample is dependent upon the first one (because you can now no longer ask a particular individual).

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But I don't mean to derail the thread - does anyone have a simple estimate of the deviation of pfr? If the Villain in the OP was 1% pfr over 1000 hands, it's a standard fold. If over 20 hands, it's a standard 3-bet. So the questions become:
1) At what number of hands does our read have to be over to justify a pf-fold? It's obviously somewhere between zero and 1000.
1) At what number of hands does our read have to be over to justify a cold-call (if any?)

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To answer your questions, I would need a read, not a HUD PFR value.

Here's a link: Sample size calculator. I'll quote you the relevant material for what we've been discussing above:

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How many people are there in the group your sample represents? This may be the number of people in a city you are studying, the number of people who buy new cars, etc. Often you may not know the exact population size. This is not a problem. The mathematics of probability proves the size of the population is irrelevant, unless the size of the sample exceeds a few percent of the total population you are examining.

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I want to emphasize the last condition because this is the part where it matters whether your samples are independent. Because they are referring to polling, they are not asking the same person twice. This comes into play when the sample is large relative to the total population. This does NOT come into play in the poker situation because each deal is independent of the others.

According to the top calculator, if you want to be 95% sure that villain's PFR is within 3%, you need 1066 hands. If you want to be within 2%, it's 2395 hands. (Be sure you give it a large population size, because this equates to independence, upon which EVERYTHING hinges.)

[Weatherhead03]

Folds. That or calling and folding unless you flopped a set.

[tiltaholic]

good discussion people.

so i posed the question mainly as a hypothetical to stimulate thought. in doing this, i intentionally left out many items that become fairly important (and which people brought up in the discussion so i won't repeat).

i was thinking of how the situation might change if we have QQ, or if the "stat read" is based on 100 hands, or 200, instead of 150. Or if there were no limpers. Or if the blinds were loose (or tight).