Once you understand basic GTO fundamentals, knowing how to play vs fish will have the highest impact on your WR.

Hand History driven straight to this forum with DriveHUD 2 Poker HUD and Database Software

NL Holdem 2(BB)
HERO ($200) [VPIP: 29% | PFR: 24.2% | AGG: 36.6% | Flop Agg: 41.5% | Turn Agg: 33.9% | River Agg: 37.2% | 3Bet: 11.5% | 4Bet: 14.1% | Hands: 325316]
CO ($61.32) [VPIP: 35.7% | PFR: 0% | AGG: 37.5% | Hands: 14]
BTN ($194) [VPIP: 47.6% | PFR: 38.1% | AGG: 53.8% | Hands: 21]
SB ($186) [VPIP: 26.7% | PFR: 13.3% | AGG: 16.7% | Flop Agg: 0% | Turn Agg: 0% | River Agg: 100% | 3Bet: 7.7% | 4Bet: 50% | Cold Call: 21.4% | Hands: 30]
BB ($282.45) [VPIP: 66.7% | PFR: 22.2% | AGG: 44.4% | Flop Agg: 60% | Turn Agg: 0% | River Agg: 50% | 3Bet: 0% | 4Bet: 0% | Cold Call: 100% | Hands: 9]
UTG ($151.26) [VPIP: 42.9% | PFR: 28.6% | AGG: 14.3% | Hands: 29]

Dealt to Hero: 5 5

UTG Folds, HERO Raises To $4, CO Folds, BTN Folds, SB Calls $3, BB Calls $2

Hero SPR on Flop: [15.17 effective]
Flop ($12): T 6 J
SB Checks, BB Checks, HERO Bets $2.85 (Rem. Stack: $193.15), SB Calls $2.85 (Rem. Stack: $179.15), BB Folds

Turn ($17.70): T 6 J Q
SB Checks, HERO Bets $12.62 (Rem. Stack: $180.53), SB Calls $12.62 (Rem. Stack: $166.53)

River ($42.94): T 6 J Q 7
SB Bets $20 (Rem. Stack: $146.53), HERO Raises To $70 (Rem. Stack: $110.53), SB Folds



I wanted to put this here because I wanted to see the difference in EV's between jamming and calling when we have a bluff catcher. I think jamming will over perform.

Hand History driven straight to this forum with DriveHUD 2 Poker Tracking Software

NL Holdem 2(BB)
HERO ($204) [VPIP: 29% | PFR: 24.2% | AGG: 36.6% | Flop Agg: 41.5% | Turn Agg: 33.9% | River Agg: 37.2% | 3Bet: 11.5% | 4Bet: 14.1% | Cold Call: 9.2% | Hands: 325316]
UTG ($243.75) [VPIP: 20.5% | PFR: 17.9% | AGG: 37.5% | Hands: 39]
HJ ($436.23) [VPIP: 30.8% | PFR: 23.1% | AGG: 60% | Hands: 39]
CO ($195.45) [VPIP: 14.3% | PFR: 9.5% | AGG: 50% | Hands: 21]
BTN ($241.14) [VPIP: 26.3% | PFR: 21.1% | AGG: 31.3% | Flop Agg: 28.6% | Turn Agg: 33.3% | River Agg: 33.3% | 3Bet: 5% | 4Bet: 0% | Hands: 39]
SB ($198) [VPIP: 24% | PFR: 20% | AGG: 25% | Hands: 25]

Dealt to Hero: Q 8

UTG Folds, HJ Folds, CO Folds, BTN Raises To $5, SB Folds, HERO Calls $3

Hero SPR on Flop: [18.09 effective]
Flop ($11): 8 3 5
HERO Checks, BTN Bets $5.23 (Rem. Stack: $230.91), HERO Calls $5.23 (Rem. Stack: $193.77)

Turn ($21.46): 8 3 5 2
HERO Checks, BTN Bets $20.39 (Rem. Stack: $210.52), HERO Calls $20.39 (Rem. Stack: $173.38)

River ($62.24): 8 3 5 2 9
HERO Checks, BTN Bets $44.35 (Rem. Stack: $166.17), HERO Raises To $173.38 (allin), BTN Folds

Just because he showed up with a bluff, doesn’t mean he’s overbluffing. I’d be careful with this mentality.

Yeah that's not what I'm doing. This was just the result from this hand.

I took a look at XR-B-B120 lines for BUvsBB for the Fish Profile.

100 hand sample size has them at 43 weak and they should be 35 weak.

Considering bluffs are a smaller portion of range than value, it's useful evidence

Pretty sure this is another spot where the OB jam is overbluffed, while non all-in OBs aren't and calling might be quite bad.

36/18 over 28, how confident are you they're a fish? Hand seems reasonably WP by them.

I don't really like that heuristic because it's not correct in a bunch of spots.

SPR is over 2 OTR. From my data in SRP's I have no spots where fish overbluff when SPR is >2. Especially in 3 street aggression lines. Do you?

Gap of 18% between VPIP/PFR is high confidence (over 96%) in my opponent being a fish over 28 hands. I have regular defined as VPIP/PFR gap of 9% or less so you can use the calculator to see the confidence level of my opponent actually having a VPIP/PFR gap of 9% or less.

I don't believe confidence intervals are accurate for sample sizes that small fwiw. Would want an explanation from someone more educated than me on that, but that is what I remember.

I should've been more clear, I meant for XR-B-B120 if it is over bluffed like your data says, you can't really apply it to this spot since most of the data will be from jams.

This is only true if your pool's reg to fish ratio is 1:1, though in this case you can be more certain factoring in cold call and 3-bet.

Are you referring to the sample of 100 or the sample of 28? Saulo used 100 as a minimum sample size in his MDA data so it's possible there is something to that.

But also it seems to me that any sample is better than no sample, so I don't think an artificial number threshold will all of a sudden make it more accurate. Even a sample of 1 is better than a sample of none.

Time to ask the statistic experts.

28....

Okay I see what you are saying there. Since most fish will have <100BB's to start with then the river bet will be an effective jam.

Another counter point is that all this data I am looking at is from non Iggy sites and bluffing frequencies are higher on Iggy which makes us want to call if it's close.

Good point on the 1:1 reg to fish ratio. I actually think there are more fish though in my pool than regs (at least on the tables I play).

technically a more accurate method would be to use bayes statistics, as in credibility intervals, off the top of my head though, that confidence interval seems inaccurate for 28 samples, the margin of error would be way bigger i feel. but in general confidence intervals are pretty reliable even for N ~25. what formula are you using?

Here's the post from Tombos
https://forumserver.twoplustwo.com/s...1&postcount=12

That would be really surprising to me. 200nl on Global is maybe 1 fish per table on average.

Hey! I made that spreadsheet.

To clarify, this was designed for measuring individual statistics. So it will work for VPIP or PFR in a vacuum, but not for (VPIP - PFR). You guys are trying to measure the confidence of the difference two dependent variables, and that requires more complex math.

I'm modelling the probability distribution using a beta distribution using alpha = 1 and beta = 1 as priors. So essentially a frequentist approach.

This approach is designed for two outcome problems, e.g. they did or did not VPIP. However, VPIP-PFR is a 3-outcome problem:

• No VPIP
• VPIP but no PFR
• VPIP and PFR

You could model this with something like a Dirichlet distribution, but that's not so easy.

First off, thanks for the calculator Tombos I use it all the time.

Okay so we need a completely different approach for a 3 outcome problem vs a 2 outcome problem? That is interesting and show's how much I have to learn.

WRT to a 2 outcome problem - is a sample size of 28 too small or is their a minimum sample size you need?

The amount of confidence you need depends on how sensitive your strategy is to changes in that stat.

For example, a 10% change to someone's 3-bet% can swing your perception of that player from nit to maniac. You need more confidence here because your counter-strategy is sensitive to small changes in their 3-bet%.

Conversely, you wouldn't alter your strategy that much against someone who c-bets 50% compared to 60%, so you don't need as much confidence.

Ultimately, I recommend being flexible. Instead of a hard "confident/not confident" cutoff, or some arbitrary number of hands, I recommend deviating more or less depending on your confidence level. If your confidence is low, then make small or no adjustments. If your confidence is much higher, then you can make more significant adjustments.

Okay so it's a sort of a sliding scale. It makes sense that a 10% swing in 3bet % is more significant because a GTO % for a 3bet % is 11-14%. Where as a GTO % for a cbet strategy is much higher.

So in my 36/18 example over 28 hands, would you adjust your strategy at all or just play him like an unknown?

I think possibly one of the flaws in my strategy is I'm using a binary approach wrt to data where as player profiles can be merged. I'm not exactly sure how to compensate for this since there's too much information to study sub profiles of reg/fish.

Ahh I see now, there were some doubts about the accuracy of this tool. Let's imagine you're measuring villain's PFR (18%) over 28 hands. What is the probability that their true PFR is <= 9%?

There are different ways to infer stats. There is not one correct method. Statistical inference is art disguised as science.

Method 1: I'm using a beta distribution, which I prefer for many reasons.

It's defined using two parameters:

• alpha = number of successes + 1
• beta = number of failures + 1

Why do we add 1?

In this scenario, they PFR'd 5 times, and didn't PFR 23 times. That gives us the following alpha and beta:


Now let's see if our soon-to-be AI overlord agrees with my spreadsheet's assessment:

]

This method is more confident for low-frequency stats.

--

Method 2: Binomial Distribution:


Now you could instead use a binomial distribution. This will give you a lot more variance because outcomes are discrete. Here there's no such thing as villain having a 9% PFR. After 28 hands, they either have a PFR 2/28 ≈ 7%, or 3/28 ≈11%. The binomial probability of a true 18% PFR occurring <= 2/28 times (shown in red) is 9.8%.



This approach is less confident with low sample sizes, because of the discrete nature of binomial stats.

I would recommend making adjustments vs this player (assuming the 28 hands were 6-max). Their VPIP alone is already quite telling. Start small - move your indifferent decisions and close hands towards how you'd play against a fish.

idk about that specific math equation, but chat gpt is notoriously bad at math

you left way too much interpretation there and it could have screwed up

the second answer it gave was also wrong

A+ post.

I'm watching the video now on why we add +1. I had heard of Laplace's Demon before just from random physics podcasts but I had never heard of Laplace's rule of succession.

Very interesting!

Okay back to watching the video.

What version was that? I feel like GPT4 is a lot better at this stuff than GPT3.5

To be clear, I calculated that 3.97% using my spreadsheet, with math, as shown earlier in the post. Then I asked GPT and got the same answer. So unless you figure we both screwed up and got the same answer, I think it's a fair confirmation

yeah that sounds reasonable, but i would only use it to confirm calculations never as the only solution

i tried applying gpt as a shortcut to my own work quite a bit and it'll lie left and right

If you prompt it to write out the step by step instructions in how it gets the answer, the math problems will solve with better accuracy.

that's a great tip, thanks