I was reading this GTO Wizard article on an AKQ toy game where they claim is the A which gains ev, when I was expecting the K or at least both A and the K.











This made me wonder how relevant is this for real poker and if the nutted hands are actually the ones who benefit from a block betting strategy.

I guess this could have a simple answer, simulating a river spot both with and without a block betting strategy, and given the one with a block betting strategy should yield more EV overall, to which hands is this EV going. Sadly I don't have access to a PC with a solver right now.

Have somebody done this? And what's your opinion about the topic?

Thanks!

First, try to figure out why KK is betting at all.

It never gets called by worse, it never folds out better, it always folds when getting raised, yet it bets some of the time. Why do you think that is?

This is not block betting it's just betting for value with AA. If they allowed OOP to jam it would do that.

In real poker middle strength hands do benefit from block betting.

No, it wouldn't. That's what makes the AKQ-game so deep and fascinating!

Do all combos of AA or just one same for both players.

There's only one combo of each hand, so if I have AA, you can't have AA.

When we have KK we are always up against AA or QQ. We never get called by worse and never fold out better, yet we still bet some of the time!

But you fold out QQ and they sometimes bluff you off the best hand.

I guess AA juts extract more value with smaller bet.

But when we bet, villain can still bluff-raise us with QQ and then we pure fold KK vs the raise.



But yes, what you said is still basically the reason why we're betting KK.

It almost sounds like something a fish would say, but sometimes it's GTO: "I bet because I don't want to get bluffed"

The AKQ-game is definitely twisting my brain.

Really interesting, now, the only way for this strategy to work is indeed to block bet KK, otherwise, villain would never raise QQ and we would rather just jam AA/QQ at the right frequency.

KK is actually indifferent between options, one reason to block bet may be "not being bluffed", but it also comes with its cons, as the other line comes with its pros and cons yielding the same EV.

It seems to me in this scenario, a reason to have a block betting frequency at all with KK could be to increase the EV of AA by incentivizing QQ to raise.

(If one could isolate a reason like that, I think this way of thinking is often used because AA bets are dominant pure strategies here, so the other hands are the ones “helping”, but I have read too at the end is all numbers and everything working together).

This seems crazy given a raise would make us fold, but given there are pros too on this line, and the EV of checking is the same, and we will have more AA than KK when block betting, is a freeroll EV gain for our AA.

Just as on one bet AKQ toy games, we bluff QQ at some frequency to incentivize calls from KK and get more value from AA, even though we lose our bet when we are bluffing and get called.

Now on real poker scenarios though, a block betting strategy seems way more holistic working in all senses including raw EV itself, with some medium strength hands simply having the highest EV by block betting when comparing it to check or bigger bets, we get the benefits of being the first bettor and being able to value bet thinner with our medium hands (something that doesn't exist in the AKQ game with KK), we protect this range with some strong hands and benefit from raises attacking the medium strength hands, and so on, different hands benefiting one way or another working on synergy.

The article does emphasis at the end of 4 flush boards, and how a correct response from villain would increase the EV of our nut hands. I think it probably does to some of our medium hands too, on all block betting spots probably even adding the 4 flush boards too.

Also with passive pool tendencies which are common on some stakes, medium strength hands could be the ones benefiting the most from a block betting strategy, because of being less punished with bluff raises than optimal, compared to nut hands which need a correct aggressive response to yield the expected EV.

About the first AKQ comments, probably KK incentives to bet are actually not being bluffed, but QQ raises keep it at bay until it reaches indifference, which at the same time are a happy result for AA, so the whole strategy ends like that all working together fine in such equilibrium.

For "one bet AKQ games", I was trying to refer to the game where you have A or Q, and villain has a K.

And on these scenarios, I think thinking on A bets as mandatory, for being a dominant strategy, and then some bluffs betting for the incentive to get the pot while villain keep us at bay with some K calls which at the same time give EV to our A is useful.

Similar to the toy game we are discussing, a method to mentally reach at the equilibrium, while understanding it's all working together.

Well KK is a bluff catcher so it doesnt gain ev
In real life usually you have hands in between nuts and bluff catchers (thin value bets) that don't exist in this toygame and that would be the main hands benefitted by the size

In this particular toygame you need to block because the opposing player has the nuts very often, if you bet big you would get a range fold when you have AA and a 50% call when you have QQ

Yes, when you have the nuts your opponent doesn't, but when you bluff he does, and therefor he constructs his MDF around having AA versus your betting range.

He doesn't fold range when we have AA and bet 0.5x pot. He still needs to call 1/3 of his KK.

EV(AA|Bet 0.5x): 1.5*(0.33/2) + 1*(1.67/2) = 1.083

But the fact that he can bluff-raise us makes AA want to block.
When we bet 0.25x pot, he calls 60% of his KK and raises 6.7% of his QQ.

EV(AA|Bet 0.25x): 1.25*30% + 1.5*3.3% + 1*66.7% = 1.092

If villain can only call or fold, then betting 0.25x is lower EV for AA:
1.25*30% + 1*70% = 1.075

Which is why this becomes our strategy if we force villain to only call or fold:
AA and QQ polarize and KK blockbets pure.



However, if we had to choose between 0.25x and 1x, then AA also prefers 0.25x.

Interesting discussion, I kind of got it until the last part.

Why do you think AA prefers 0.25x instead of 1x when we don't allow villain of the chances of raising, and the same doesn't happen when comparing 0.25x with 0.5x?

Thanks!

For the reason aner0 mentioned: when we bet too big, villain can simply fold everything but AA.

Remember, in this toy game, hands are exclusive. When we have QQ, villain will have 50% AA and 50% KK.

When we bet 1x pot, MDF is 50%, so villain only needs to call AA to make our bluffs indifferent.

So when we value bet AA, villain ends up folding 100%, since he always has KK and QQ, and he doesn't need to call any KK to make
our bluffs indifferent.

So the EV of betting 1x pot with AA is: 100% * 1 = 1x pot

But when we bet smaller than 1x pot, villain must call some KK to make our QQ bluffs indifferent, which gains us additional value with AA.

**************

It seems 0.41x pot is the optimal bet-size in this case: https://www.desmos.com/calculator/w4g7m504j3

X = bet-size
C = call%
K1 = how many KK combos must call
K2 = what proportion of the calling range is KK
Y = EV

Oops. I meant, what proportion of the total range is KK that calls.

Really interesting, I got it, thanks