Analyzing a raise which is not all-in

[eastbay]

I think anyone who's been paying attention over the last six months or so has a good idea of how to analyze open raises all-in. Raises all-in over raisers or limpers are a more or less trivial extension of the same ideas.

I think we've reached diminishing returns in that kind of analysis. I'd like to move on to some questions of the next level of complexity.

In particular, with medium to deep stacks, we know from experience that raises all-in are probably not the biggest $EV play for most hands. Raises to 2.5x - 3x BB are the standard line for many hands. Can we justify this choice analytically? Can it be improved upon or adjusted to game factors?

Let's start with the following scenario:

You're on the SB with A7s, and it's folded to you. Game is off-bubble, so let's work chipEV for the time being. Stacks for you and BB are 1000, and blinds are 25/50.

What's the chipEV of a raise to 75? Assume an opponent who plays like you would in his spot.

This is not an easy or cut-n-dried question by any means, but I'm hoping we can get a quality discussion going on how to make a reasonable estimate at it. Please don't just post a flat guess. I'm much more interested in a post that doesn't arrive at a number if it offers an interesting line of reasoning about how to proceed.

eastbay

[eastbay]

Raise to 125, not 75.

eastbay

[AleoMagus]

Where before, with analyzing all-in raises, we had three possibilities

1) steal
2) get caught and win
3) get caught and lose

and these three possibilities were easy to completely analyze

% steal*amount won
% win when caught*amount won
% lose when caught*amount lost

We now have a much more complicated situation. We now need to consider:

1) Steal % (straightforward, same as before except obviously we might get called by a different range of hands)
2) We are raised sufficiently that we need to fold (again, this is actually pretty straightforward. We simply define a range of hands that will raise us here, and a value to which we will need to fold. We can even assign a probability to which a person might raise/cold call certain hands like KK or AA
3) We are called/raised and play a flop/hand and lose
4) We are called/raised and play a flop/hand and win

3&4 obviously make this very much more complicated than before. These aren't even really single possibilities, as we will need to separate the times we are called from all the times we are raised and call.

Then there is the fact that we cannot easily say A7 wins x amount on average vs a given range of hands. In the all-in scenarios, this was easy. In this case, we might need to assign arbitrary values for this (like a modified odds of flopping an ace when opponent doesn't have a higher ace, etc...). Even just assigning arbitrary values here could get really complicated when you factored in everything you would need to to get even a rough estimate.

A couple of other possibilities here might be using extensive data compiled from tournament summaries (how many time you won the hand after seeing a flop with A7) or even just writing a basic bot-type program and using it to play a huge number of hand simulations.

My option of choice here is to use tournament summaries to get some idea. If I remember, you wrote a program of some kind which evaluated the results of all your all-in situations. If one could do the same thing for each independent hand (like pokertracker does, except street by street) then after a significant sample you would actually have a pretty good idea of your EV after called on a steal with any given hand.

Once all of this data is together, the calculation would be easy I suppose. The hard part is trusting this data

For example, If I could assume the following:

-I will get called 10% of the time
-I will get raised and call 5% of the time
-I will get raised and fold 5% of the time
-When called, my avg EV is -20t vs 10% range of hands that calls
-When raised, my avg EV is -80t vs the 5% range of hands that raises such that I can then call

then I could calculate as follows:

Fold equity=%fold*1BB
=.8*50t
=40t
Caught equity when reraised and need to fold
=.05*-125t
=-6.25t
Caught equity when raised
=.05*-80t
=-4t
Caught equity when simply called
=.1*-20t
=-2t

Total equity
=40t-6.25t-4t-2t
=27.75t

Bear in mind, I don't take these assumptions seriously, I am just using them to show how I'd go about doing this analysis.

Once we have these kinds of assumptions, we can then start to experiment with different sizes of raises to see if one or other generated a higher profit. Changing the sizes of the raise would certainly change a lot of other variables, and we would have to make reasonable modifications (like tightening or loosening up the range of calling/raising hands and our avg EV if we see a flop).

Oh well. That's where I'd start anyways, but it's going to require a lot of assumptions or data accumulation to draw any real conclusions anytime soon

Any thoughts? Way off track or heading in the right direction?

Regards
Brad S

[chill888]

Complex question. A mathematical answer is beyond me. Just a couple of minor thoughts.

If I am small blind and trying to steal versus big blind with a 2.5xBB raise:

1. I think there is +EV of never trying to steal when blinds are low - to train the guy that you only bet with a good hand. Then you can more easily steal when blinds are higher. If I have a good hand early on and bet, I will usually flash my cards so he knows I wasn't stealing.


2. Knowing your opponent is essential. Some guy always defend, some never defend, most fall somewhere inbetween. Trying to steal against guys that always defend is dangerous early on.

3. Assuming I have a reasonably tight image (which I usually do), and the BB isn't the loosest guy ever born, then: It is HUGELY +EV to ALWAYS (99.999%) bet post flop the exact same amount as the steal attempt REGARDLESS OF THE FLOP. (How you proceed if called or raised is more complex). In any mathematical model, this behavious will be a significant factor on whether the steal attempt is +EV.

4. Remember in this situation that you are IN FACT trying to steal. Don't ever get in an all-in cat fight early in the tourney with not much -- just because you know he doesn't have much either. We have all bumped into a BB with AA or KK while we are pushing 3rd pair no kicker to the limit. Sometimes steals don't work. Don't go broke trying to disprove this.

gl

[eastbay]

You have been paying attention. /images/graemlins/wink.gif

Your thoughts are nearly identical to mine so far. However, I think we can modify the original idea somewhat to make the problem slightly more tractable.

Let's make stacks/blinds such that any re-raise is almost certainly all-in. This eliminates the whole branch of "re-raised/call/play flop".

Let's go with stacks of 1200, blinds 50/100. Now if you raise to 250, I don't think there's many players who will raise other than all-in often enough for it to be a significant part of the analysis.

So we've got now:

1) opponent folds
2) opponent re-raises all-in
2a) we call
2b) we fold
3) opponent calls and flop is played

Let's go one step further and say that as an initial first cut, let's move in every time on the flop. There's 600 in the pot, and we've got 950 in our stack. A sort of reverse stop-n-go.

Then we have to figure what villian will call with, and determine how often he hits it with each holding.

EV = P_fold_preflop * EV_fold_preflop +
P_reraise * EV_reraise +
P_seeflop * EV_seeflop

P_fold_preflop, P_reraise, P_seeflop come directly from the choice of hands for each option. EV_fold_preflop is obvious.

EV_reraise = P_wecall * EV_wecall + (1-P_wecall)* EV_wefold

P_wecall is a function of our holdings plus what we think of the other guy. As a start let's say we plan to eject if re-raised all-in. P_wecall = 0, so this scenario is trivial.

Now the harder part:

EV_seeflop = sum P_opp_hand * EV_opp_hand

EV_opp_hand = P_call_allin * EV_call_allin + (1-P_call_allin) * EV_fold_allin

P_call_allin requires us to determine calling standards for our opponent. You could choose a few canonical opponents:

1) calls w/ A high here
2) calls w/ any pair or better
3) calls w/ top pair or better
4) calls w/ TPTK or better

If they call, you still have to enumerate the boards to determine EV_calls_allin.

That's the whole thing. The rest is mechanics. I think this is worth pursuing. When I get some code in place to do the probabilities, I think we can talk in a little more detail about the strategy choices, and draw some conclusions about this sort of play.

eastbay

[lorinda]

One thing that is interesting about this setup is that you have to keep all raises the same size for it to work (at least initially) because changing the raise size automatically would tip off your opponent as to the strength of your hand.

I am not clear as to which route you are heading here, are you trying to work out an optimal, and always the same, raising size given that you are going to raise OR
an optimal raising size for each hand, given that the size of the raise would alter the play of an intelligent opponent who knew what you were doing?

Lori

[eastbay]

[ QUOTE ]
One thing that is interesting about this setup is that you have to keep all raises the same size for it to work (at least initially) because changing the raise size automatically would tip off your opponent as to the strength of your hand.

I am not clear as to which route you are heading here, are you trying to work out an optimal, and always the same, raising size given that you are going to raise OR
an optimal raising size for each hand, given that the size of the raise would alter the play of an intelligent opponent who knew what you were doing?

Lori

[/ QUOTE ]

There's a number of things you could look at once you get an idea how to get a number.

I think one of the more practical q's is on the decision to raise all-in vs. a raise to 2.5xBB (or whatever), as potential alternatives in a situation where you've got something like 10-15xBB in your stack.

This is a grey area that I wonder about quite a bit while playing.

eastbay

[rachelwxm]

The proper math is beyond me I think you ask a question only you can answer /images/graemlins/smile.gif but I offer some of my thoughts anyway. /images/graemlins/cool.gif

One thing I know why reraise all in not proper here from sb is a result from (0,1) game. Assume two people playing HP one bb is 5% of stack, I think the correct strategy is push with 10% of hands and call with 5% of hands.

Poker is not exactly (0,1) game, but we see if bb called your push with 5% of hands, it's negative EV for sb to push all in.

I don't know how to model raise 3bb if the above is not already obvious to you. /images/graemlins/smile.gif

The set up is maybe we assume bb is either call or reraise all in. If he call no post flop play is allowed.