Hey. Thanks for taking the time to do this I really appreciate it. (Also thanks for the harsh realization that I don't play perfect poker, I was pretty happy in my bubble)

9:35 the 9h5h hand: You really only want to worry about which hands you're making indifferent with your bluffs (unless of course we wouldn't be able to come up with enough in the spot, which would make us want to bet smaller because he wouldn't ever call vs the big bet). The bet size you chose with your value bets comes from running your hand across calling ranges for every size and picking the one with highest ev. I thought we might be isolating too strong of a range by jamming, so I just went for the bet size that targeted Kx(My thinking here is that he will bet some Kx ott, and check some Kx otr so his Kx region is reduced and by blocking some of the lower flushes the hand just works better as a small raise). I would be curious to see what ranges you used for the BB in your tree, and also whether he needs to be defending bare Kx ever vs the jam. I think assigning a range to the bb in this specific spot otr is pretty difficult and requires a lot of guesswork.

17:10 I am for sure overbetting 99 and 77 here absolutely. I was a little hesitant with JJ as I said in the video. I've actually never heard of Monker, does it solve for multiway pots? I don't really like range check here, we have all 3 sets and none of our opponents should have T8o, so we won't have a great disadvantage, and I think we want to be putting money in the pot before board changes and it's hard to get value.

20:10 Again as I said in the video my thinking was that when we block the Ax region which makes up a decent chunk of the continue range vs small bet and we unblock all of his high frequency Jx continues (KJo QJo JTo J8o J7o), as well as all the straight and flush draws the hand just benefits from large bet. Seems that this effect isn't really significant enough. With such wide ranges pio probably just figures it can get a bunch of money out of all of these Jx hands on basically any turn anyway, so it's not concerned with putting the money in early. I'd be curious to see whether tighter ranges make my logic more applicable.

Thanks again for the lengthy response.

Cheers.

9:35 the 9h5h hand: You really only want to worry about which hands you're making indifferent with your bluffs (unless of course we wouldn't be able to come up with enough in the spot, which would make us want to bet smaller because he wouldn't ever call vs the big bet). The bet size you chose with your value bets comes from running your hand across calling ranges for every size and picking the one with highest ev.

So this is a subject that I have been very curious about in the past. Let's just stick with optimal play for a second so we don't confuse it with exploitative strategies we may choose. A lot of the stuff I am referencing is from MoP.

The 2 main thresholds that we are concerned with here would be the indifference threshold for bluffing and the indifference threshold for your opponent bluff-catching. The reason I brought it up was because from my understanding the easiest way to find the minimum bet size for your value region was to pick a set of hands in your opponents distribution that you want to make indifferent to bluff-catching. This means against a properly balanced strategy everything below this region should fold to your bets (-EV) and everything above this should defend to your bets (+EV). If we know which region we want to fold and want to call then we know what region should be indifferent to the 2 options (0EV) as well.

The question to ask would be, "Which set of hands do we want to make indifferent?" and to that we should answer, "The strongest set of hands possible without sacrificing value from our opponent; i.) easily folding too often because we sized too large or, ii.) calling too wide because we sized too small. Note that ii. is the same as us not getting enough value from his bluff-catchers because we sized too small.

I believe the question and answer above are pretty close to what is said in MoP somewhere in the "Optimal Play" section. I need to go over this a little better as it has been awhile and I am starting to take studying the game seriously again.

So after having said that, I have used my opponents bluff-catching indifference threshold to pick a size that is big enough and it has made sense in my own mind while also feeling like I am making the right decision in many scenarios.

I will continue to look for the exact paragraph in MoP as that may help us along with this discussion.

Do you think the technique I use for picking the best bet-sizing is correct/incorrect? Or do you think it has flaws? And why?

I would like to note that I start with what optimal looks like in my mind then move to exploitative after I have painted that picture clearly. That is why I would like to discuss optimal here.

Mathematics of Poker is a book that you have to be careful with applying to your own play because most of the toy games in there operate under assumptions that are pretty much never present in real poker. It's a great book to learn game theory from of course, just need to make sure you understand what is actually happening. However, it sounds like you're on the right track so I'm not too sure why you're thinking about making our opponent indifferent with our value bets.

When you design your betting range you take your value bet and you run it across opponents calling ranges using every possible sizing (this assumes he will be using a calling frequency that makes us indifferent to bluffing for every bet size) then you decide which of these has the highest ev. Once you've decided which bet sizing option is best you begin adding bluffs until your opponents pure bluffcatchers(this is important) are indifferent between calling and folding. Seems like what you're saying is that you want to make a big portion of his range indifferent, which won't be the case unless its pure bluffcatchers with no blocker effects (this is probably something you've seen in the book with the AKQ game if I remember correctly, where the calling range is just the K). In real poker our opponent will have calls with good blockers which won't be indifferent vs our theoretically correct designed range, because they block some of value bets and of course we cannot design a range that will make every single hand indifferent (every one of his hands has an effect on our range which makes us slightly unbalanced). Basically the point is that we choose a hand in villain's range that loses to all of our value bets and beats all of our bluffs and make that hand indifferent which gives us a reference point to know if we are over/underbluffing. If villain has a hand in his theoretically correct calling range which doesn't have a good blocker, loses to all value bets and it's a profitable call this will mean we are overbluffing, and he will start calling with everything that beats our bluffs.

Again, none of this will have an effect on the bet size we go for with our value bets unless we run into a situation where we can't come up with enough bluffs for the sizing we are choosing.

Mathematics of Poker is a book that you have to be careful with applying to your own play because most of the toy games in there operate under assumptions that are pretty much never present in real poker. It's a great book to learn game theory from of course, just need to make sure you understand what is actually happening. However, it sounds like you're on the right track so I'm not too sure why you're thinking about making our opponent indifferent with our value bets. When you design your betting range you take your value bet and you run it across opponents calling ranges using every possible sizing (this assumes he will be using a calling frequency that makes us indifferent to bluffing for every bet size) then you decide which of these has the highest ev. Once you've decided which bet sizing option is best you begin adding bluffs until your opponents pure bluffcatchers(this is important) are indifferent between calling and folding. Seems like what you're saying is that you want to make a big portion of his range indifferent, which won't be the case unless its pure bluffcatchers with no blocker effects (this is probably something you've seen in the book with the AKQ game if I remember correctly, where the calling range is just the K). In real poker our opponent will have calls with good blockers which won't be indifferent vs our theoretically correct designed range, because they block some of value bets and of course we cannot design a range that will make every single hand indifferent (every one of his hands has an effect on our range which makes us slightly unbalanced). Basically the point is that we choose a hand in villain's range that loses to all of our value bets and beats all of our bluffs and make that hand indifferent which gives us a reference point to know if we are over/underbluffing. If villain has a hand in his theoretically correct calling range which doesn't have a good blocker, loses to all value bets and it's a profitable call this will mean we are overbluffing, and he will start calling with everything that beats our bluffs.

Again, none of this will have an effect on the bet size we go for with our value bets unless we run into a situation where we can't come up with enough bluffs for the sizing we are choosing.

Ok. So I am going to just reiterate what I said before it got deleted but very quickly. I was trying to discuss the theory with you so MoP is applicable for the situation.

For some reason 2 chapters in MoP got blended in my mind at some point in the past. That is why I could not find the paragraph I was looking for. As soon as you mentioned the AKQ game I realized that we were talking about a river situation where absolute polarization is possible while what I had mixed up was from flop and turn situations and how to pick your bet size. And yes I agree, value regions/equity distribution is what your bet size is built around.

When you mentioned "pure bluffcatchers" I was slightly confused at first because when i think pure in poker I think of pure strategies and mixed strategies. And you were saying adding enough bluffs to make his "pure" bluffcatchers "indifferent". But after realizing that you are talking about pure polarization it makes sense to me. As if our value is better than his bluff catchers and our bluffs are worse. Got ya. Just took a minute.

That combined with the AKQ game made me realize I was blending information in my mind (and for quite some time). Anyways, I found it in the chapter "Non-static Multi-street games".. It was speaking about draw heavy board textures and how to size correctly. So it would actually apply to the J99ss hand where you overbet. And as I had mentioned in the previous post

Looks like we want to make his weak aces and weak backdoor draws indifferent OTF with the proper sizing. If we overbet we end up allowing him to easily fold these.

So using the indifference threshold is a good way to help pick a sizing OTF and OTT in non-static situations.

What MoP says in the "Key Concepts" summary on p 264 is

Some draws (or made hands) are so strong that it is impossible to make them indifferent to calling a value bet. When choosing which draw to make indifferent, the answer is often the strongest draw that you can.

I somehow blended that info with the river info which could have been really bad but thankfully it was not. Thanks for having this discussion with me as it allowed me to separate the information correctly. After using the info from MoP and solvers over the past few years i somehow got it mixed up as there is a ton of information.

PS No I wasnt saying make a large portion of his range indifferent. And yes I agree with the blocker/card removal effects. This is how card counting in blackjack and similar games operates more-or-less as well.

Hey. With such wide ranges our opponent will still have to call very wide even vs the overbet, so my thinking was that since we block a bunch of the small bet continue range we want to go bigger. As user_name points out with some pretty good proof this was a mistake, so your thinking was correct. I went a little deeper into it under his response ;)

Cheers.

Pio likes to use overbets in spots where the board is dynamic and hand strengths are likely to change on the turn, so boards like Q84tt, 962r, 843tt. Of course this will change depending on positions and ranges.

The mistakes I see kind of depend on the player. Most guys just end up grossly underdefending vs overbets, and to be more specific they just rarely ever raise, where pio usually end up raising ~10% of the time vs 115-120% sizing (of course all dependent on the exact spot). Seems that players have a difficult time understanding that there isn't that much of a difference in defending frequencies between a 90% sizing and a 120% sizing, probably influenced by the fact that so few regulars use overbetting strategies otf.

Hey. Thanks for the kind words.

Yes, in theory choosing only a single suit would cost us EV. I doubt any of the top regs actually randomize things like this properly, it's obviously very difficult. If you really want to be perfect you can use some kind of random number generator or even use a clock as a randomizer (if the second hand is in position x you do y), however the way games play currently you are almost never going to run into a player where this will be important. You mostly just want to focus on how your opponent is deviating from optimal play and shift your whole strategy to exploit it.

Cheers.

Hey,

I wouldn't say it's a "very" bad flop for us, and it's definitely not a fantastic one for HJ which is why I wouldn't be a big fan of checking 100% here. HJ having basically only 99 at a 100% frequency (JJ 3bets at least some and 77 dicey call vs Mp2) isn't going to have a very aggressive betting frequency. For that reason we aren't gonna have an opportunity to XR much and allowing 2 ranges to see an additional card here is pretty costly for JJ. If somehow the BB and HJ were reversed and we could check into the BB I could be on board with 100% check.

Cheers.