Okay here is the hand in question.

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

NL Holdem 2(BB)
HERO ($200) [VPIP: 28.9% | PFR: 24.1% | AGG: 36.7% | Flop Agg: 41.9% | Turn Agg: 33.8% | 3Bet: 11.6% | 4Bet: 14.2% | Hands: 305760]
SB ($434.01) [VPIP: 0% | PFR: 0% | AGG: 0% | Hands: 1]
BB ($201) [VPIP: 100% | PFR: 0% | AGG: 50% | Flop Agg: 0% | Turn Agg: 100% | 3Bet: 0% | 4Bet: 0% | Cold Call: 100% | Hands: 1]
UTG ($233.53) [VPIP: 0% | PFR: 0% | AGG: 0% | Hands: 1]
HJ ($71.54) [VPIP: 0% | PFR: 0% | AGG: 0% | Hands: 1]
CO ($211.11) [VPIP: 0% | PFR: 0% | AGG: 0% | Hands: 1]

Dealt to Hero: 9 8

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

Hero SPR on Flop: [17.73 effective]
Flop ($11): T A 4
BB Checks, HERO Checks

Turn ($11): T A 4 6
BB Bets $15.68 (Rem. Stack: $180.32), HERO Raises to $52.00

Okay so I know from MDA that this spot has a turn B150-F frequency of around 38%-39% in these positions and the Ace high filter is around the same. If I run the numbers in MDF the numbers come out to 26.68/78.68 = 1-34% so 66% MDF but 34% fold frequency

So I have a 4%-5% discrepancy between what my opponent should do and is actually doing.

A few questions:

1. Does MDF work OTT like it does OTR? If not why?

2. Is this a profitable raise if the above is true? If not, how much of a discrepancy would we need to start raising hands like this?

GTO Wizard prefers call/fold but not huge EV differences in raising.

Well it's not a great raise - you're repping a pretty thin hand range - 66 or maybe 46 as most other value hands will bet small on the flop - and if you were going to bluff, as we should have 1 bluff combo for every value combo I think we can do better than 98 off.

You're also facing an overbet, and I would just fold. I can't imagine calling is a great play unless you will play perfectly on the river, and who knows if you will. I'm not really sure what this guy should be over betting here, but you have 1 hand on him. I would be over betting some sets for sure and perhaps a combo draw as bluffs.

I can't see this play being a winning strategy long term.

I think you've got it backwards, should be 66% folds, 34% calls

• Alpha = $52 / ($52 + $15.68 + $11) = 66%
• MDF = 1 - Alpha = 34%

No, because your bluffs have equity once called. Imagine if villain defends exactly MDF. That means all your pure bluff raises break even. All the low-equity trash in your range that's "supposed" to fold could just raise instead, breaking even on the raise and freerolling their river equity.

For that reason, the solver will always defend wider than MDF facing a raise on earlier streets. You can confirm this by studying flop or turn reports.

No. It sounds like they are severely under-bluffing and under-folding in these spots.

• Breakeven Fold% (Freeroll territory) >= 66%
• GTO Fold% is around ~57%
• Actual Fold% is around ~38%

If this is true, then optimal play is to raise value heavy.

However, before you make big adjustments, I recommend double-checking your data. Ensure you're calculating and filtering it correctly. Grouping all the B150-F into one category might not be optimal since the alpha depends on your raise size. Try breaking fold% down by the raise alpha, and don't read too much into low sample sizes.

Lol TY Tombos I had a feeling I messed this up.

I also had a feeling MDF was different on earlier streets but didn't know the exact reasoning.

Okay Tombos this is not the exact spot but pretty close COvsBB filters for BB OB Turn probe and also folding frequencies. They are severely under folding here so we should never raise as a bluff?

It depends on how much equity bluffs have. If bluffs have a lot of equity folding frequency should be small.

Also should be interning to look fold frequency after they call turn. Maybe there is an exploit there.

To add to what Tombos said, even if population was somehow folding more than alpha, it doesn't necessarily mean you want to raise all your air. Sometimes calling can be even better, eg if you have info that someone is playing the river too straightforward after you call (betting strong hands, mostly checking with air). Then, floating turn to bluff the river becomes a very nice option.

Basically you win a similar amount the times that villain is bluffing, and save a ton of chips the times he happens to have a strong hand.

So OB/OB is overbluffed in general in this line so don't think we should be floating turn with air.

I need to check out OOP SRP BC range composition and then river fold frequencies as well.

Okay I'm back with some more data as I'm trying to understand this spot.

I had my CFP guys filter the raising by sizing so we can see how much under MDF they are folding.

So this is BBvsBU specific, BB folds 52% vs 3x-4x sized raise, so that still seems not enough right? They should be folding 66% (although like you said they over defend in GTO relative to MDF so this number should be lower but 52% still seems too low correct?)

I also had them filter by sizing so B150-F is 53%. There are huge samples on these so I'm confident in the numbers.

Is 57% the GTO number OTT for folding frequencies?

Unfortunately, my CFP didn't have enough sample size for the river in this spot to see if they overfold there.

Okay so bluffing turn sucks that has been established, but what about bluffing river? Let's say BB OBs turn/OB's river. Let's see folding frequencies here since we already know OB/OB is overbluffed, although this does not necessarily mean it is overfolded as I have learned.

So I'm wondering if this is profitable?

Can't we just fold turn - lose $5 and avoid all this?

I also thought we started the hand with $200 effective - and the sizes don't add up to $200.

As for bluffing river, I suppose it's not the worst bluff, but I don't see how he folds anything other than air. I'm for sure not folding 2 pair+, but you will get me off JQ type hands. I'm never getting to the river though, as i'm just folding the turn and the hand would be over.

The guy over bet the turn and we have a gut shot with 9 high, just let him have it.

Keep in mind the Alpha changes considerably depending on your raise size. I cooked up a quick table in sheets to demonstrate:



I've highlighted Alpha for raising 2x, 3x, and 4x, facing a 150% pot bet. If you min-click with pure air you need them to fold about 55% of the time, whereas a 4x raise requires 71% folds to break even.

In reality they should defend wider to prevent you from freerolling your equity with draws. Like we saw earlier GTO was defending about 7% wider than alpha. And from the data DDP has posted, it sounds like they are over-defending this spot (most likely because they were under-bluffing to begin with).

What does your MDA say about folding% and bluffing% in this spot, DDP?

Yeah for sure we can just fold turn, I actually did fold turn in game. The above is a made up hand to explore something I've been thinking about, thanks for catching my error I forgot to add $52 to my stack.

Awesome table Tom! I will be looking at that and trying to compare it to some MDA I have.

Okay so first things first. For the purposes of the discussion I am assuming BB goes X-B120-B120, there is a huge distinction between this sizing and X-B150-B120 (this is closer to GTO). The former is overbluffed so we will be using those sizing's.

As an aside, I asked Saulo about the concept of if a spot is overbluffed, does that mean it is by definition overfolded? Here was his response.



Okay now let's look at the MDA. The main problem is the sample size. Basically no one X's flop, calls B120 and then jams over another B120. But here is the data I was able to get.



So they fold 64% of the time in the aggregate, that's a 353 hand sample (not great but workable). I think what you have to do here is go down the bet sizing list and multiply the sizing's by the sample and figure out what the actual aggregate bet sizing is - then we can compare that 64% to MDF and see if it is overfolded.

What do you think?

Edit: Here is turn data as well. I just want to double check that they in fact overdefend vs turn raises.

I did the math since we can't get B120 OTR for sample sizes, we need to use the aggregate sample. The aggregate sample bet size is B76.5% (maybe check my math here) and they fold 64%.

So let's say 5.5BB OTF X/X.

OTT: X-B6.6 (B120) C6.6

River is 18.7BB

76.5% of 18.7 so 14.3BB

We raise 3.5x to 50.05BB

50.05 / 18.7 + 14.3 + 50.05 = 50.05/83.05 = ~60%

So it looks they overfold by 4% if we use 3.5x sizing for raising. It seems reasonable, even if we use 4x raise sizing it's only 63% fold at MDF.

I'm not sure how scientific this is but I think a sample size of 350 hands is meaningful.

@tombos21 Let me know what you think

The Bad News

After reviewing the data more, I think you can't conclude anything about how often they fold to a raise, unfortunately.

River:

It looks like most of your fold-to-raise data is taken from the times BB overbets turn, then downbets river. Almost all of your data is taken from the times they bet less than pot on the river:


The weighted average of bet sizes that faced a raise (highlighted) is around half-pot. Unfortunately, these smaller bets' range construction looks much more merged compared to OB. There's no reason to assume their folding after overbetting a polar range would be similar to these smaller bet sizes. Furthermore, you don't know how often each of these bet sizes faced the raise, so you can't accurately work out the average bet size on the river to deconstruct this grouped stat.

To find fold% here you'd probably need to expand your filters to include more data, perhaps looking at all OOP PFC spots taking a similar line, then filter for the fold frequency by bet and raise size.

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Turn data suffers the same problem. This isn't showing you how often they overbet turn then fold to a raise, it's showing you how often they bet turn for any size then fold to a raise. That's a problem.



Here's the table for Alpha of 3x-4x raise after betting any size between 1/4 pot and 5x pot: as you can see, the Alpha varies between 38% and 77%. So it's hard to say if they're overfolding here.



The best way to do it would be to filter the data for fold-vs-raise after 150% turn probe, or some group like turn probe 130%-160%.

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The Good News

It does appear that the X-OB-OB line is very over-bluffed, and you don't need any further data to see that. Focus on what you know. You can't be sure if they're overfolding to a raise, but you can be pretty confident that they're bluffing too much.

You could try some very gnarly exploits here like calling down far too many static bluff-catchers lol. Idk exactly what hand classes these color-codes correspond to, but this is just far too bluffy by any reasonable definition of "weak hands".

Damn!

Okay thank you Tombos so I will try to get more specific data - I need Overbet turn then fold to a raise data specifically for OB turn not just any turn bet sizing- right?

Thanks for the breakdown, I feel like one needs a strong grasp of statistics to understand all this but you are helping me a lot and I appreciate it.

My CFP has told me that weak = low pair.

I'll focus on the good news .

We do know this is Overbluffed so should I just be calling strong Ace high's down here or how would you adjust to this? Do I call more turns relative to GTO or less if I know I am going to get barreled OTR more often but also with a weaker range.

A lot to consider here but this was fun and I will report back with **hopefully** better data.

I almost feel like just studying GTO is easier than trying to merge GTO and MDA. At least with GTO I can just check my little solver and be done, there's so many more layers when you add how population is playing + proper filters etc

The data doesn’t tell us anything about what to do with A-high, it only tells us we should call with hands that beat a bluff. Eg if most of the bluffing range is weak 1p, then calling with A-high would clearly be losing.

As for how wide to call the turn, that’s a little more complicated. River overbluff doesn’t necessarily make you want to call wider OTT, because most of the EV of the turn call really comes from the times BB gives up the river. So you would need to know population’s river checking frequency after turn overbet, in order to come to any sort of conclusion.

Yeah my Ace high example wasn't good. Thank you for that. I will get river checking frequencies after turn overbet (my MDA discord must hate me because I ask like 5 questions a day haha).

@Tombos21

Okay I have data for X-B70F BBvsBU. Can we now figure out if turn probes are over/under folded? I think the chart would be a bit more practical if we used more diverse sizing's from 10-150 so like 25/33/50/70/100/120/135/150 etc.

Data is here:



Edit: Also in the process of getting X-B120F data for BBvsBU to compare.

I ran a few turn reports in GTO Wizard to find the average GTO folding% after probe 66-75% facing different raises.



A surface-level analysis shows that your population data is pretty close to GTO. Might need to get finer buckets, or look elsewhere for overfolded spots.

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I'm quite surprised they haven't already done this type of analysis for you! Seems like the most obvious first step with MDA would be to find clearly overfolded lines

Wow that is surprising, thanks for running those reports. I still want to check on the X-B120F Data if that's okay with you. I'll relay that data when I get it.

Yeah so basically we have something called the Game Plan. It's split into 12 major game trees. So OOP PFC/IP PFC/OOP PFR/IP PFR for 2bet/3bet/4bet pots.

There's MDA for all major lines in all 12 game trees. It's an insane compilation of data but it's still not as granular in a lot of spots like this.

I wouldn't be surprised if higher stakes guys like 1knl+ we're getting data like the one you showed but 200nl guys like me aren't going to qualify just because we aren't making them enough money for it to be worth it (at least that's how I am assuming they are viewing it).

Okay TY Tombos! I will report back with X-B120F Data and anything else I can think of that could help us.

That was quick! Okay samples aren't great but here is X-B120F Data.

I checked a few spots in the XX - B125 F line in GTO Wizard. Here are the approximate GTO Folding frequencies vs your population data:



Again, it looks like the population is pretty close to GTO here. But I didn't check all the sizes.

I've been learning some new statistics skills lately. When dealing with lower sample sizes, it can be helpful to assign a standard error to a stat, so you know how reliable it is. Here are the standard errors of your population data:






--

• The 68% confidence interval (± 1SD) indicates the stat falls between that range 68% of the time.
• The 95% confidence interval (± 2SD) indicates the stat falls between that range 95% of the time.

For example, the B70 Fold 5-6x Raise = 69% ± 7%, meaning you can be 95% confident that the actual population folding frequency is between 62% - 76%.

(Assuming no prior information about what the stat "ought to be")

This is impressive stuff Tombos. Thank you for the demonstration.

I'm still in literal awe of how much lower the GTO% OTT is compared to the Alpha (and also sad that population is basically defending close to GTO, so much for exploiting that spot!). That was definitely very educational for me to learn that GTO doesn't come close to Alpha OTT.

I'm excited for a GTOW video from you on this topic, I actually have some more data coming through tomorrow on a different spot and was wondering if you could take a look at it to help me figure out this 0 EV spot.

It's basically a C-B-BF spot and a solver likes both jamming and calling and I was trying to figure out which option was better. I'll pm you the thread and the data when I get it.

Keep crushing! This standard of error stat is a game changer.

Thanks again!

You could probs take this a step further using the frequencies and standard error you guys are talking about here, and find 95% confidence intervals for the EV of jamming and calling otr.

If the 95% confidence intervals don't overlap, then you can conclude there's evidence that the EV's are significantly different from one another. If they overlap, you can't really draw statistical conclusions (at a 5% significance level) about which one is better from your data. That's usually how hypothesis testing works in statistics.

In general, I think you should also be looking for no overlap between confidence intervals from MDA frequencies (i.e., estimate +- standard error like tombos) and gto ones in order to draw conclusions about pop deviations. And conclusions are always limited by how close the data is to the exact texture and bet sizes.

Yeah I just received the data and it's pretty crazy but the position is BBvsSB SRP and the line is C30-B70-B70 and I jammed and wanted to see fold frequencies OTR. The data only has a sample of 727 hands (the DB is huge too which makes it disappointing) but the folding frequencies line up exactly with what Alpha should be, 72%.

I think I need to just stick with really really common lines for now because sample size is just too much of an issue to be conclusive. Oh well back to GTO.