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pot odds and realizing equity problem

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pot odds and realizing equity problem

Hey,

I can't quite wrap my head around the problem of how do I know if I am making a profitable defend or not.
For example, say SB is opening 50% in 6max if folded to and we have 75o in BB, if he opens to 3x we need 33% equity to call, however 75o has 32.5%, now obviously this is a close spot and won't matter much, but if we change SB opening to say 60% we now have 35.1% equity. From that it should be clear that given we are IP + pot odds we should be calling, however we often don't get to realize our equity and will get barreled off our hand etc. My question is, is there a way to factor in possible postflop outcomes, or should I be approaching this by making the best play on each street, so say on a flop of T52r villain bets 3/4 psb, so 4.5 into 6bb meaning it has to work 43% for him to bluff ATC meaning we need to defend by raising or calling at least 57% of our range (which given that we "should" be defending 75o here means we will be defending about 70% pre of which like 10-15% will be 3-bet probably).

That however will amount to roughly 600 combos pre, 57 of which will be around 340 combos on the flop which is quite a lot. This example got slightly carried away and doesn't quite illustrate my problem as well as I would have liked to perhaps, so why cant we defend like AJo in BB vs UTG 15% opener when we have roughly 40% equity, how much equity of that will we get to realize and how to quantify it is my question I suppose, both for IP and OOP.

Hope someone can throw me a bone here, thanks !

6 Comments

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d0zer 11 years, 11 months ago
Also, am I correct in saying that if SB is opening to 3x then if BB folds more than 62.5% we are making a profit opening ATC ? (at 5-10, risking 25 to win 40 so 25/40=0.625) That number seems awfully low : o
d0zer 11 years, 11 months ago
and same goes for stealing from BTN, if SB fold to steal x BB fold to steal is more than 57% we should be profiting by opening ATC (if we min-open so risk 20 to win 35=57%) ?
GameTheory 11 years, 11 months ago
1. You should focus on maximizing profit with your entire range, not on realizing equity with marginal hands by calling down a ton and figuring out how often you need to call to make your opponent indifferent between bluffing and giving up his worst hands.

2. Calling preflop with 75o in position has more value than to just hit a pair and get it to showdown. When you call you stay in the pot and get to see a flop and how he reacts to it. You should often try to bluffraise him or (double) float him when you think he is weak.

3. If your opponent opens 60% you should start 3-betting him at a very high frequency. If you 3-bet from 3x to 9x, he needs to defend more than 1/3rd of his range, or a 20% range against 3-bets to keep you from 3-betting any hand (ignoring card removal). 20% is roughly 22-AA,A8-AK,KT-KQ,T9+, so that is extremely wide.
If he defends this range by calling you will also have a very profitable cbet on most flops, lowering his equity even more.

4. You don't need to have 33% equity to call. For instance someone raises UTG with QQ-AA, and you call on the button with 55-99. The flop is 952r. You only have 30% equity with your range here, but it would be incorrect for you opponent to call, since 66-88 don't (have to) call, since they only have 2 outs. And against sets they can't bet. The correct strategy here for you is to count his cbet as dead money, and start raising him with both your sets and your bluffs. You must bluff with a frequency to make his entire range indifferent between calling 0, 1, 2 or 3 streets. Thus you can bluff a lot on the flop, up to your entire range on the flop and geometrically decrease your bluffing frequency on each street. Where you overbet bluff/value bet on the river as long as no Q,K,A has come, overbetting is here is optimal since your opponent never has a better hand and you either have the effective nuts or no showdown value at all. Overbetting allows you to bluff with a maximum frequency and maximizes your value.

5. Conclusion is that you can call and/or 3-bet 75o as long as you make the right moves against his range and don't focus on calling down small pairs.
d0zer 11 years, 11 months ago
i would still like to know the answer to the math comments i made and also in your point number 4, why do we want to construct a raising range ip on 952r (or was your example meant literally as utg having QQ-AA and we having 55-99 exactly?)

maybe someone else can still shed some light on this stuff
GameTheory 11 years, 11 months ago
It could be that the T52r flop is good for his range bad bad for yours, whereas 876hhs would be good for you. Range assymetries can break these rules such as defend at least 43% unless he can bluff any hand.
Also this rule has very little value. Suppose he bluffs QJo and it works 45% instead of the 43%, then it follows that betting QJ has positive expectation, say that its EV would be 1bb.
But his might achieve a higher EV by checking, for instance 2bb.

If he bets all his air hands like that he actually could lose money, even though you are not defending enough to make it unprofitable for him to bluff QJo if he was forced to openmuck the turn if you call.

This simple math just does not work for real poker!


why do we want to construct a raising range ip on 952r (or was your example meant literally as utg having QQ-AA and we having 55-99 exactly?)
My example was an extreme case of range asymmetries. Pot odds are almost completely trown out of the window in that case. This happens to a lesser extent in real poker. Mostly 10+ handed FR, tight UTG player opens preflop and cbets a flop with medium cards.
GameTheory 11 years, 11 months ago
why cant we defend like AJo in BB vs UTG 15% opener when we have roughly 40% equity, how much equity of that will we get to realize and how to quantify it is my question I suppose, both for IP and OOP.
Suppose UTg opens to 3x, you need to call 2bb for a 6.5bb pot, 2/6.5= 30.7%.
This equity is relative to the pot on the flop.

Say the flop comes A52r, he cbets with a large part of his range, now you have to call since your equity went up to 75% against his entire range. But against the best 20-25% hands of his range you only have 20% equity so you are forced to start check calling him on multiple streets. This allows him to effectively bluff many hands, against which you have to fold AJ with a positive frequency.
Therefore you will not realize your full 40% preflop equity, since calling with a dominated range allows him to run multistreet bluffs against you.

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