Theory thought (range merging, sort of but not really)

[LearnedfromTV]

So I had a thought about range merging or whatever you call it, and then it morphed into something a little different about how we construct ranges. I don't think it's incredibly deep, but I thought it was interesting enough to make a post.

That whole discussion focused on the river, where hand values are absolute - you're either ahead or not, and pot odds are only relevant insofar as my hand beats x% of the hands he's betting, so I call/fold/whatever.

But pre-river the situation is different because whoever is behind has outs. There are definitely times when you can make a bet that make a better hand fold and a worse hand call, and where the opponent can be correct to do both given your range.

For example, say you have if you have AK-high with one heart on a board of Q [img]/images/graemlins/heart.gif[/img] 9 [img]/images/graemlins/heart.gif[/img] 6 [img]/images/graemlins/diamond.gif[/img] 3 [img]/images/graemlins/diamond.gif[/img], and bet 3/4th pot, which also puts you allin. Your opponent has either J [img]/images/graemlins/heart.gif[/img] T [img]/images/graemlins/heart.gif[/img] or 22.

Versus your range, the JT should call and the 22 should fold. Versus your hand, (with 19 outs) the JT is definitely getting correct odds to call, so you would prefer he fold, but you still make money from the call (just less than if he had folded). And 22 folds incorrectly versus your hand but correctly versus your range.

But this isn't quite as good as the situation you get in when you shove a dominating monster draw versus a range containing another "monster draw" or a weak pair. I.e. You shove Q [img]/images/graemlins/club.gif[/img] J [img]/images/graemlins/club.gif[/img] on Q [img]/images/graemlins/heart.gif[/img] 8 [img]/images/graemlins/club.gif[/img] 5 [img]/images/graemlins/club.gif[/img], your opponent has KQ or 7 [img]/images/graemlins/club.gif[/img] 6 [img]/images/graemlins/club.gif[/img], and because your range is overpairs, sets, and the occasional draw, the opponent incorrectly folds KQ and incorrectly calls with the sf draw. Or if you have A [img]/images/graemlins/club.gif[/img] K [img]/images/graemlins/club.gif[/img] on Q [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/heart.gif[/img] 5 [img]/images/graemlins/club.gif[/img], vs 7 [img]/images/graemlins/club.gif[/img] 6 [img]/images/graemlins/club.gif[/img] or a bunch of weak made hands, you're in better shape vs. the draw, but the made hands fold and the draw calls.

Now, I realize in all these cases, the opponent is making the correct decision versus your (perceived) range, and so if everyone is accurate about perceived range, the fact that he folds better and calls worse is just a weird consequence of you having a particular hand in your range. And I know that this probably seems like standard "fold equity" stuff, i.e. donkament style we like shoving AK preflop to get 66 to fold and AQ to call.

But I think what I'm getting at is a little more fundamental than that. From a reciprocity perspective, if we were all game-theoretic maximizing robots we would all be constructing ranges that contain equivalent amounts of this phenomenon; i.e. your shove range has AK too, and I have to fold 66 when you shove AK too, etc. But of course we all don't have identical ranges; that's where all the profit (or loss) comes from. The point of all this is that I'm guessing that searching for situations like those described above and trying to create ranges that maximize the likelihood that you get in these kind of spots is worth a lot. It basically amounts to having a particular goal when disguising how often you actually take certain actions with hands in your perceived range, and is a fancy way of saying "get your opponents to make big mistakes".

Along those lines, a similar hypothetical is having a line you take with sets be a line to which your opponent assigns a range much less weighted toward sets; point being, you make money in that spot because he incorrectly assigns a range, but particularly in that case you make a lot of extra money, because tricking him with a set significantly changes his EV vs. the range.

Thoughts?

[Overfloater]

another way to describe it:

case 1:

Villains range: [17 rock, 43 paper, 40 scissors]
Heros range: [61 rock, 5 paper, 34 scissors]

[mythrilfox]

well some of this reminds me a little of what i read in aba's well post, where he said that his biggest "aha" moment in poker was realizing that you should push hands that fare well against his calling range, and not his actual range. the JT/22 example kinda reminds me of that, because there its obviously much better to push with AK over 55, even though 55 is a bigger favorite over both those hands.

but other than that it seems really no different from a basic river situation. the only equity hands have in pots is their % to win anyway, be it from cards to come or from being the best hand a certain amount of time. in other words there is no difference between assigning hand ranges and figuring out how often you're ahead than assigning hand ranges and figuring out how often you're going to win the pot w/ x cards to come.

and i dont get the robot part

[LearnedfromTV]

[ QUOTE ]
and i dont get the robot part

[/ QUOTE ]

Maybe a bad way of putting it; all I meant was that if everyone played perfectly, that perfect play would include individual hands where this would take place (you shove with a specific hand where because of your range your opponent is correct to call worse and fold better), but overall it would even out, because you would get to do this to your opponent exactly as often as he gets to do it to you.

[LearnedfromTV]

[ QUOTE ]
but other than that it seems really no different from a basic river situation. the only equity hands have in pots is their % to win anyway, be it from cards to come or from being the best hand a certain amount of time. in other words there is no difference between assigning hand ranges and figuring out how often you're ahead than assigning hand ranges and figuring out how often you're going to win the pot w/ x cards to come.

[/ QUOTE ]

theoretically, maybe, but there's a practical difference between

- being at the river with a specific hand and having your equity percentage versus a range be an aggregate of having either 100% equity or 0% equity

- being on the flop with a hand where your equity percentage versus a range is the aggregate of stuff like "25% equity 50% of the time, 55% equity 25% of the time, etc."

Because on the river the only thing to estimate is how many hands better than yours and how many hands worse than yours are in his betting range (or calling range if you're betting).

But on the flop, range weighting, in terms of assigning likelihoods to various two-card combinations, is only the first step, and in many cases your equity is particularly sensitive to how accurate you are with respect to a certain subset of those combinations.

Put another way, on the river with one pair, it doesn't matter if he has a set, two pair, or a better one pair, on the flop it does. So even though you narrow his range as the hand proceeds, it's actually earlier in the hand where it matters more that you know how the range you're facing is weighted.

[mythrilfox]

well i mean this is all true i guess, but it seems kinda random and i don't see how it's practical

[DJ Sensei]

A few months ago I was playing and a hand came up that made me realize that some situations are just favorable to one player or another. (Situations involving 2 or more players hands and a particular board, and that even if one player has the better hand he'll almost never win the pot when its played out in a "standard" way)

but I never tried to do any more thought or research to it, or figure how to alter my game so that I got into more favorable situations, cause it seemed like it would require a lot of work, and I reckon it sorta gets done automatically by the nature of my evolution as a player. If theres anything to take from the matter, position is almost always pretty sweet.

[Geir74]

[ QUOTE ]
well i mean this is all true i guess, but it seems kinda random and i don't see how it's practical


[/ QUOTE ]
My thoughts also.

Your first example doesn't represent something new:
I try to avoid floating flops with unimproved low pocket pairs (unless I'm planning to bluff), because nearly every other hand is drawing to a minimum of 6 outs against me, and i have two outs when behind.
Likewise I fire second barrel more often with overcards if i know that my opponent have a floating range that includes low pocket pairs.

Your second example comes down to:
If my opponent have a lot of suited gappers in his preflop range, we should play more suited aces and suited high cards against him.
BUT, I think position is so importent when it comes to drawing types of hands, that I'm not sure how useful this concept is.

[LearnedfromTV]

[ QUOTE ]
well i mean this is true i guess, but it seems kinda random and i don't see how it's practical

[/ QUOTE ]

This describes like 60% of my interest in poker. [img]/images/graemlins/smile.gif[/img]

I do think there's something practical here, focusing primarily on postflop frequencies, not "calling more preflop with suited aces," although I can see where you got that idea. The examples I gave were just that, examples.

I like DJ Sensei's point, especially because the majority of pots don't see showdown anyway.

///

Kind of an aside, I'm not a good chess player at all, but I have a book (Silman) that teaches through talking about position/piece/etc imbalances not as inherently good or bad, but as opportunities to be recognized and manipulated. Clearly something similar is true of poker and hand ranges. When your range is of similar strength to your opponent while differing in some certain way, it's like having a knight to a bishop; it could be a wash, or one side could turn the difference into an advantage. Way too theoretical I guess, but like I said that's half of what I like about poker.

[freemoney]

i think its a good post but i have always thought the best player is the player who has the biggest difference in his range vs. his perceived range which is what you hit on later in your post when talking about sets.