2nl SNAP 54s OTB

[DJAbacus]

Holy Sh*t, you're right, that River call is awful. I was so concerned about whether I should be raising OTF that I completely overlooked the dreadful call OTR.

Incidentally, Villain shows up with A 7 which just goes to show that a 2nl, you can't even take VPIP/PFR stats too literally even over 500 hands.

Make a note, learn from it, move on.

[MadMojoMonkey]

which just goes to show that a 2nl, you can't even take VPIP/PFR stats too literally even over 500 hands.

500 hands is a laughably small sample at any stakes.

[DJAbacus]

500 hands is a laughably small sample at any stakes.

Really? We're not talking cbet Turn % we are talking VPIP/PFR

[MadMojoMonkey]

Really? We're not talking cbet Turn % we are talking VPIP/PFR

Grain of salt.

Use the stats as guidelines, but realize that the person could be running either hot or cold over any number of hands. The more hands you have, the more it tends toward the mean.
As the number of hands tends to infinity, the error bars tend to be infinitesimally wide.
The error bars get tighter and tighter on these stats (they are convergent).

However, a 100% confidence interval will ALWAYS include a range of 0% to 100% (non-inclusive), because it is mathematically possible that any sample (from a hypothetically infinite population) is an anomoly, no matter how large the sample.

[DJAbacus]

Grain of salt.

Use the stats as guidelines, but realize that the person could be running either hot or cold over any number of hands. The more hands you have, the more it tends toward the mean.
As the number of hands tends to infinity, the error bars tend to be infinitesimally wide.
The error bars get tighter and tighter on these stats (they are convergent).

However, a 100% confidence interval will ALWAYS include a range of 0% to 100% (non-inclusive), because it is mathematically possible that any sample (from a hypothetically infinite population) is an anomoly, no matter how large the sample.

I realise this, but you are saying that a sample of 500 hands is too small with regards to an accurate VPIP/PFR read.

VPIP/PFR stats of 13/9 of course doesn't mean that a Villain raises the top 9% of hands, this only means that a Villain raises 9% of the time and we assume that this is the top 9% of hands. It is highly likely that these 9% of hands are strong hands.

[DJAbacus]

Maths Question for Mojo.

A player puts money into the pot with the top 50% of hands.

What is the probability that this players VPIP = 10% over 500 hands?

What is the probability that this players VPIP = 30% over 500 hands?

What is the probability that this players VPIP is between 40% and 60% over 500 hands?

[DJAbacus]

Maths Question for Mojo.

A player puts money into the pot with the top 50% of hands.

What is the probability that this players VPIP = 10% over 500 hands?

What is the probability that this players VPIP = 30% over 500 hands?

What is the probability that this players VPIP is between 40% and 60% over 500 hands?

Not going to do the exact maths but the answers in simple terms are:

1) extremely unlikely

2) unlikely

3) highly likely

In conclusion, VPIP and PFR stats are pretty reliable over a sample size of 500 hands.

[MadMojoMonkey]

I realise this, but you are saying that a sample of 500 hands is too small with regards to an accurate VPIP/PFR read.

VPIP/PFR stats of 13/9 of course doesn't mean that a Villain raises the top 9% of hands, this only means that a Villain raises 9% of the time and we assume that this is the top 9% of hands. It is highly likely that these 9% of hands are strong hands.

Obv. we assume villain has the top 9%, because if we're wrong, then we have even more equity than we had estimated.
This is completely beside the point.

The math says that 9% is only as "accurate" as ~6.8% to ~11.8% @95% CI - which is a pretty wide difference in poker ranges.

6.8% = { 88+,ATs+,KJs+,AQo+ }

9.2% = { 88+,ATs+,KTs+,QJs,AJo+,KQo }

11.5% = { 77+,A9s+,KTs+,QTs+,JTs,ATo+,KQo }

and that's just at 95% CI... which means you expect to be wrong 1 out of 20 times you assume the range is this tight.

Do you see what I mean by grain of salt? Yes, the odds of Villain's actual range being 11% is less likely than 10%, but both are still well within the realm of possibility that is predicted by the math.

The tighter the bounds you set, the lower the CI, and the higher the CI, the wider the bounds.

When you say, "The stat says 9%, so the range is 9%." then you have a 0% CI. (Well, you have very low CI, since we're talking discreet math).
If you want a 100% CI, then it always extends from 0% to 100% (non-inclusive).
These are not helpful.

For any meaning from the stats, you have to allow for uncertainty. No, not uncertainty. It's certainty. When we choose a 95% confidence interval, we are certain that our error bars will be too small 5% of the time. That's the point. We accept that there will be error, then we quantify how much we are willing to accept. Once we know that, we cut off the appropriate amount of the "tails" of the distribution.

The variance is the same, no matter where we cut the tails, but the level of confidence we have in the results will choose what parts of the distribution count as the "tails."

We can't get less than 100% CI without cutting off the tails. When we cut off the tail, we allow/expect to have results that fall outside our confidence interval. It is by choosing a good confidence interval that we make practical use of a statistic.