2nl SNAP 54s OTB

My game is definitely improving so really looking for leaks and I feel that a big leak of mine is not raising OTF when I'm ahead. I'm too passive in these spots and too happy to slow play call when I should be fast play raising.

This hand I just played is a good example. I should have raised OTF. Then maybe raised OTT as well, so just left with a call OTR which I'm sure was a good call but.....

Villain is a reg 13/9 nitty reg over 500 hands. I put him on overpairs, sets, TPTK, Missed FDs like KsQs.

888 Poker - $0.02 NL (6 max) FAST - Holdem - 6 players
Hand converted by PokerTracker 4

Hero (BTN): $2.02
SB: $2.14
BB: $1.33
UTG: $3.56
MP: $1.04
CO: $2.05
SB posts SB $0.01, BB posts BB $0.02

Pre Flop: (pot: $0.03) Hero has 5 4

UTG raises to $0.06, fold, fold, Hero calls $0.06, fold, fold

Flop: ($0.15, 2 players) T 4 5
UTG bets $0.11, Hero calls $0.11

Turn: ($0.37, 2 players) 7
UTG bets $0.27, Hero calls $0.27

River: ($0.91, 2 players) 7
UTG bets $0.68, Hero calls $0.68

[F] If you'd raised (I agree you should have), the Turn would probably have been checked to you (you bet). If he bets again on the Turn, I doubt you want to be raising again against the player you describe since his sets are likely starting to dominate his range ...not sure about this, those flush draws are still out there
What if he 3Bets?

[R] You only beat his bluffs at this point. Are you expecting there to be enough of those to justify calling?

Raise flop, raise turn, fold river. You need to really look at the river because "you're sure it's fine" and it's not really close at all to being a call.

Villain is a nit, so I'm leaning more towards fold PRE. Raise flop, raise turn, fold river.

Agree with Spoon, river isn't even close. He's 13/9, which means he's probably like 9/9 UTG or something. Take a reasonable range for UTG being 9/9 AND triple barreling this board and pokerstove that with your hand. It shouldn't be close. You realize you got counterfeited right?

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.

Originally Posted by DJAbacus

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.

Originally Posted by MadMojoMonkey

500 hands is a laughably small sample at any stakes.

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

Using the Wilson Score Interval to provide sensible error bars:

13% = 65/500
Using a confidence interval of 95%, the "true" value of the underlying stat is 10.3% to 16.2%.
At 99% CI, it's 9.6% to 17.4%.


9% = 45/500
Using a confidence interval of 95%, the "true" value of the underlying stat is 6.8% to 11.8%.
At 99% CI, it's 6.2% to 12.9%.

Originally Posted by DJAbacus

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.

Originally Posted by MadMojoMonkey

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.

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?

Originally Posted by 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.

Originally Posted by DJAbacus

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.

Originally Posted by DJAbacus

Originally Posted by 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.

I'm not clear on your parameters, so I don't know what you're really asking me here.

Here's my best guess, given my assumptions:
1) 7.07(10)^(-80)%

2) 5.28(10)^(-18)%

3) 99.9993%

4) What is the probability that this players VPIP = 50% over 500 hands?
4) 3.4%

Note that question 3 is of a completely different sort.
I answered 1,2, and 4 with the Probability mass function for a binomial distribution.
Question 3 requires the use of the Cumulative distribution function for a binomial distribution.

How long before you realize you're talking to someone with a minor in mathematics who knows exactly what he's talking about and actually use this resource to learn something instead of testing your instructor's mettle?

Originally Posted by MadMojoMonkey

How long before you realize you're talking to someone with a minor in mathematics who knows exactly what he's talking about and actually use this resource to learn something instead of testing your instructor's mettle?

Let's leave it here Mojo,

I believe that a players VPIP/PFR stat over 500 hands is going to be fairly reliable and waving a piece of paper in front of my face with a Maths Qualification on it isn't going to change that, sorry.

I agree with the others. Raise flop, raise turn, fold river. River call is diabolical. Why did you call the river?

Originally Posted by seven-deuce

I agree with the others. Raise flop, raise turn, fold river. River call is diabolical. Why did you call the river?

Still thinking for some reason that I beat Premium pairs. I'm becoming more aware of paired boards now.

Originally Posted by DJAbacus

Let's leave it here Mojo,

Let's let the mods do the modding, DJ.

Originally Posted by DJAbacus

I believe that a players VPIP/PFR stat over 500 hands is going to be fairly reliable

I believe it, too. I believe that numbers and logic exist, and the rest just tumbles out. That's math.

I'm trying to help you out with the "fairly reliable" part. I gave you some ranges which quantify that statement and links it to poker in a way that you can use to make $$.

When I say the 9% could represent any range in this ballpark:
{ 88+,ATs+,KJs+,AQo+ } through { 77+,A9s+,KTs+,QTs+,JTs,ATo+,KQo }

I'm saying that because I have quantified the facts.
1) Villain may be playing a tighter range and "running hot."
2) Villain may be playing a looser range and "running cold."

VPIP and PFR become more reliable with more hands (like most poker stats you'd use in a HUD). With these, the variance is asymptotic toward 0 in the long run. It's just that "the long run" is vague and under-stating it. It doesn't guide us, it only warns us.

"Let's stop jumping at shadows and quantify that shit!" - Anonymous mathematician

There's really a lot of steps involved to explain why I'm using the Wilson Score Interval for the stats, but if you click here, you'll see that it's a stable estimator (not proven to be an unbiased estimator, but there isn't one for this stuff) for this kind of statistic obtained from Bernoulli trials.

Originally Posted by DJAbacus

and waving a piece of paper in front of my face with a Maths Qualification on it isn't going to change that, sorry.

Nor should it. I'm sorry for this. It's like some cheap intellectual bullying and it's a piece of shit move on my part.
You've caught me in a difficult week. I accept your judgement on this issue.

***
Use any RNG worth it's salt and give it a 9% rate and run it for 500 trials. See how many successes there were and divide by 500 for the %-age.

You'll see that the 9% runs hot and cold. It's a random variable. We wouldn't call it that if it didn't run hot and cold.

So that 9% produces a spread of results at the end of the 500 hands.

We look at that spread at the end and we say..."hmm... what else might look like 9% after 500 hands?"
So we run the trial for various numbers near 9%. We see what range of those produces a spread that overlaps 9% (that's 9% exactly, not the 9% spread).

This tells us the 6.8% - 11.8%. It means that any "true" value of Villain's range in that ball park may look like 9% after 500 hands. It tells us that it is very unlikely that Villain's true range is tighter than 6.8% or wider than 11.8%.

This is huge knowledge.

Thanks Mojo...you are a gentleman and a scholar Sir...

Agreed - these kinds of two pair are never good when villain shows riv aggression like that. Snap fold riv.