[Closed] QJs river bluff ?

I think I'd check it behind on the turn because they look very SD-bound & we won't make any better hands fold here, they will probably bring Ax & Kx to showdown. The only thing is that we can gather value from various draws but as we consider ourselves behind & can take a free card that will help us more than it will help our opponents I think we should do it. And on the river check behind UI as well.

i don't like checking on the turn. mp3 does always have overcards like KJ KT Ax. he is almost always unimproved and on this turn we can very well represent T8 or we could have just called 7x on the Flop. when Mp3 checks he will give up his hand most of the times and since CO checked as well he indiciated to have nothing either. certainly he is on some draw as well. with your outs to the flush and good bluff opportunities on straightcards it's kind of a must bet on the turn. double bet is absolutely fine and riverbet is mandatory against AT KT! Nh!

Aren't we worried by their WTS values? Will they fold their Ax & Kx with some degree of certainty?

You got great odds. ~1:9 for your bluff and he could have just called with A8 KT KQ or something like that and you can represent a hand very well so if you decide to bet the Turn you have to bet the River again to make them believe that you got it and on 280 hands the WTS can still vary a lot and his real wts could be just 41 40 or something. for a valid WTS you need a big sample size.

Can you please advice sample size based on which we can judge about WTS? I have some troubles with this issue...

i forwarded this thread to another handjudge who is better at statistic.

I wrote something about this back some time but it is in german. For those who can read german it is here: https://forums.pokerstrategy.com/de/forum/thread.php?postid=1461199#post1461199

That is a lot to translate, so I will only outline the result for the specific question and the principles how the result is derived.

When you ask how big a sample size should be for a statistic to be significant you look for an interval of the upper and lower boundary of this statistic and a probability value for this interval which you can trust. Basically the larger your database is, the more narrow the interval is around the true value of the statistic and the more probable it is that the true value really is in that interval.

This can be done if we look at the error which a statistic has. Luckily for us, the numbers in poker behave like the standard probability distribution, at least for large samples. This makes things simple as the error depends only on the sample size and the value of the statistic. In the standard probability distribution a standard error is defined as the error interval within the first standard deviation. This translates to a 67% probability that the true value of the statistic is within the error interval.

If you want an error with more confidence you look for the error to be within the second standard deviation which translates to a 95% probability for the true value to be in the error interval.

When the measurement of the value is 43% (WtS 43) the standard error is:

SE = sqr [0,43 * (1-0,43) / sample size]

This is the error within the first standard deviation. 67% confidence is not much, so you may want more. This is easy as the error within the second standard deviation is

SE2 = 2*SE <-> SE = 1/2 * SE2

You should also note that the sample size in the formula is not the number of hands but the number of events the statistic is based on. For the WtS this is equal to Flops seen. To get the number of hands we have to divide the sample size by the VPIP.

But we want to know the sample size needed, not the error. The error is a variable that we choose. We have to transform the formula a bit:

SE = sqr [0.43 * (1-0.43) / sample size]
-> SE^2 = 0.43 * 0.57 / sample size
sample size = 0.43 * 0.57 / SE^2

For the SE2 (confidence 95%) we get

sample size(SE2) = 0.43 * 0.57 / SE2^2
sample size(SE2) = 0.43 * 0.57 / (1/2*SE)^2 /* with SE2 = 1/2 * SE, see above */
sample size(SE2) = 0,43 * 0,57 / (1/4 *SE^2)
sample size(SE2) = 4* 0.43 * 0.57 / SE^2
sample size(SE2) = 4 * sample size(SE)

So to get the confidence for the error from 67% to 95% we have to quadruple the number of hands.

Lets say we want the error of the WtS to be in the interval [0.41, 0.45] with a 95% confidence.

SE2 = 0.02
sample size(SE2) = 4* 0.43 * 0.57 / 0.02^2 = 2451

Number of hands needed = 2451 / VPIP = 2451 / 0.22 = 11141 > 11k

This is an awful lot of hands, so we may want to settle for less.

You explain it ♠_thumbsup: I don't know German but with the help of translator I learned interesting things from your posts. Luckily my technical education allowed me to understand what's written here in English and there in German. Thanks a lot for your efforts!

oh, idk how i missed this one. really interesting to consider a semibluff/barrel here. there are lots of river situations that are neat to consider. I think we have to commit 2 barrels here the vast majority of the time and need to be able to represent a lot of made hands that can value bet the river thin.

As for this discussion on sample sizes required for stats, I think using a kind of confidence interval around a given descriptive stat is great as long as you're prepared to think about the kind of standard error you're working with (and the big amount of variance this creates).