Hi guys,

Don't know if this is the correct place, so if this is the case please tell me the correct section.

I would like to ask if my math/thinking process is correct.
I'll give an example:

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Data:
Equity vs OP calling range = 30%
% of time OP fold to a bet = 50%
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Q1: is my bet +EV?


Equity of my bet= Fold equity (FE) + Equity
FE = OP equity if he call*% of time OP fold to a bet=70%*50%= 35%
Equity of my bet=35%+30%=65%
IF I bet 5 on a pot of 5, the min P need for win 50%--> my bet is +EV
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Q2: Is my all-in semibluff +EV?

Same assumption of above.

I don't know if it is correct to compare, assuming that the data above are taking into consideration that we are going all-in, the Equity of my bet (65%) with the min P need calculated using as total pot the current one + effective stack, OR just the current pot.
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Thank for your help!!
Cheers

Adding fold equity to card equity makes no sense to me. In your example, making a pot size bet with villain folding 50% of the time gives you an EV >=0 assuming showdown. The EV equation is

EV= fe*Pot + (1-fe)*(eq*(Pot + 2*Bet) - Bet),

which says if fe=0.5 and Bet=Pot, you can play any two cards for EV>= 0.

This equation is most applicable for all-in since no further betting is assumed. For Bet > Pot, you can solve for the break-even card equity or put the equation in Excel and use its Goal Seek function. For your example, the breakeven card equity with fe=0.5 is (Bet-Pot)/(Pot + 2*Bet). So, if the all-in bet is four times the pot, the needed equity is 33%.

Yes totally agree with you, it make no sense to me too.

What about using this method in order to take into consideration FE and estimate if my bet is +EV:

1. Tale Total pot size times our equity.
2. Subtract the result from step one from our bet.
3. Examine the reward to risk ratio and see if OP will fold the needed % of the time

The EV equation I posted has 3 variables – fe, eq, Bet. If you set EV to 0, you can solve for one of them for breakeven given you know or can reasonably assign values to the other 2. Conversely if you have estimates for all 3, plug the values into the equation to see if EV is positive. Note positive EV is good but maximizing EV is a lot better.

Basicaly any your cbet smaller than potsize is +EV.
Semibluff with draw and no SD value needs less FE to be +EV.
On the other hand when your equity is SD value check may be better than cbet, here it is more equity realisation than cbet EV.

Great! every thing clear, thanks.

Tell me if I'm correct, in all our discussion we always assuming that we go to SD right?

How can we evaluate if an action is correct by removing that Hp, that is we want to evaluate the next street. From what I'm understating we are quite incapable since the decision tree is really big. Am I right?

Correct.

In an EV blog I wrote the following;

6. What about a situation that is not an all-in bet?

When future betting is possible, the decision tree can get very complicated and there is little chance an accurate EV can be calculated. Nevertheless, by assuming a showdown situation at the time of the current decision, you have a first cut estimate of how well the hand stacks up against the risks and rewards of betting; that is better than no quantitative analysis. Furthermore, you may be able to estimate how much you might win (or lose) on a future betting round if you hit your outs – this is called implied odds, so some account for future action can be made.

So, all-in bets and final river bets are amenable to detailed EV analysis. Drawing hands like four flushes can include implied odds. In some cases the future actions may be very limited (e.g. a player is very short stacked) so the decision tree is simple. For the rest, take the results as a first cut approximation to be modified as applicable for non-math factors, which should always be done.

Now it make sense, could you please give me the link of your blog post, Im really curious..

Moreover, Im reasoning on our ability to evaluate on the flop our action since i think that we have to many variables, i.e the tree is too big, and therefore we are not able to accurately evaluate our action. In details, Im reasoning on two main strategic implication and i would like to share them with you and see what is your opinion.

The first one: given that the tree is too complex in order to evaluate a Flop bet with a semibluff, isn't it a good strat to play the flop quite loose, with a lot of check/calling and then on the turn where the tree is more simple evaluate our decision and see if a semibluff is profitable? Even if I think that with some hands we have to (semi)bluff on the flop no matter what in order to be balance with our strong hands, if its not the case we will be quite exploitable.

The second one: given that we are reasoning with probabilities calculated by assuming that we arrive to SD isn't it more correct to play our flop (semi)bluff with always the goal of going all-in in order to realize the equity and be consistent with our assumption? (always by taking into consideration to be balance and not exploitable)

Thanks for your time.

Rather than give you my non-professional opinion, I suggest you get the book Expert No Limit Hold’em by Will Tipton who views the poker decision problem through decision trees and develops a GTO line of thinking you might find appealing.

pksmv's two questions are basically identical: shouldn't I stick around to the turn/river when the decision tree is sufficiently pruned?

Just 2-3 hands of calling your adversary's heavy flop bets, and your hand not improving on the turn, effectively ends your tournament (or your working day, if you allot a daily max loss for cash games). Under the infinite cash/time assumption, yes, by all means call to the river. But take this notion to the logical extreme. Just go all-in pre-flop every hand. When the sun explodes, you'll have broken even. Why not use this pathological strat to, as you say, "realize your equity"? Same reason why you shouldn't as a rule call big flop bets to narrow the tree -- you don't have infinite cash (see St. Petersburg Paradox for an interesting result under the infinite cash assumption).

In this case, the simple rule works. If your opponents make it cheap to call, call/check. Otherwise, fold. What is "cheap" enough? Well, that's why poker is hard.

Thanks for your suggestion! Much aprecciated!

You are right, that reasoning is fine with the strong assumption of infinite cash/time.
Thank for your obs!