What I'm Reading

Wednesday, February 14, 2007

Defending Your Raise

This is something I've had (and still have) tons of trouble with-- you raise it up before the flop and somebody comes over the top of you for a decent amount. Defend? Give up? Jam?

I feel like because my opening standards are relatively loose, this happens more than it does to a more solid player and I have been laying down too much.

Let's look at some numbers.

Say I raise UTG (assume 6 max for the ranges I'll give; full ring < watching paint dry). The game is .5/1 and I make it 3 to go. Now suppose the button reraises me the size of the pot. He is raising me another $7.5, and is risking $10.5 immediately to win $4.5 immediately.

So, for our button reraises, he has to win 4.5x for every 10.5 he risks, where x is how many more pots he has to win immediately (this, of course, is assuming that if he is called, he loses exactly what he raised. We'll go into more detail in a minute).

So 10.5/4.5 = 2.33. So the button needs to win only 2.33 pots preflop for every time he is called, or (1/2.33) 30% of the time.

What this means is that even if when you call you automatically win the pot, he is still profiting if you fold over 30% of the time.

Now let's make this example a little more realistic. Suppose that when he reraises and is called, he wins 50% of the time and you win the other 50% of the time. How often do you have to call preflop in order to prevent him from exploiting your tightness?

In order to find the breakeven point, set the function to 0 and use x to be the % that we call preflop

0 = -3(1-x) + 12(x/2) - 10.5(x/2)

-3(1-x) = when we fold preflop = we lose 3 dollars
+22.5(x/2) = half of the time we call, we win the pot, netting 12 dollars
-10.5(x/2) = half the time we call, we lose the pot, losing 10.5 dollars.

Solving for x, we get .8 or 80%. That means in a more realistic situation, we have to be called a very high percentage of our preflop raises. Of course, this is overly simplified because you have to take into account many factors (how your opponent plays, your hand, if the raise is from the button or the blinds, etc.) but these results are nonetheless pretty eye-opening.

The following range is a standard LAG opening-raise requirement from UTG in a six-max game (22+,A2s+,K8s+,Q9s+,J9s+,T9s,ATo+,KJo+,QJo). [by the way, I got this range from Chipp who in turn had based it off of something Andy Bloch had written a while back].

This is 19.2% of the hands. 80% of 19.2 is 15.36% of the hands, or 77+,A7s+,K9s+,Q9s+,JTs,ATo+,KTo+,QJo.

Of course, this can be skewed a bit in order to include hands that are easier to play PoF, 22+,A8s+,KTs+,QTs+,JTs,ATo+,KJo+.

Still, I can't imagine KJo being something you can call a reraise preflop with. Even if you are only calling iwth 1/2 of the hands, your range [88+,A9s+,KTs+,QTs+,AJo+,KQo] still includes a lot of hands that seem like the easiest mucks in the world. I think what accounts for this (aside from the ex-showdown value of the hands is that your opponents AREN'T raising so often in order to take advantage of your weakness in calling reraises. I suppose if they were, calling with QTs would be automatic.

Regardless though, I think that I am both raising preflop too often and not defending enough of these raises. Hopefully this work'll get me a little closer to playing PF more optimally.

If I have time/remember/can figure it out, I will in the future do similar examples involving defending against these raises but try to make them more realistic.


lucko said...

To me what it should more show is the value of the RR. Also if you are getting RR'ed a lot, nothing says you can't RRR light.

One major factor is what the active image doing for us. Hopefully its helping us getting our big hands paid. Not sure exactly how to quantify that, though in these calcs.

NFulton said...

That's something I definitely should've touched on. I've widened up my own reraising/re-reraising range a lot and my results have improved since having done so.

I dunno if this is because of my active image or not, but last night I got walks two rounds in a row while holding AA. But then again, I also CRed the river with the nuts to get called by a five high flush with a four-flush on board.

Ryot said...

Hey man, you said you wrote a program could you send it to me cheers mate.

Anonymous said...

Your math is not correct.

If the reraiser wins 4.5$ everytime you fold and loses 10.5$ everytime you call, the break even point for him is at

4.5*p - 10.5 * (1-p) = 0 => p ~ .72

that means 72% of the time he needs you to fold.

Chipp said...

Re-check your math chief, precisely .7 is correct.

And fulton, initially I had the same thought of just assuming a 50/50 split on the pot, but I think that's clearly pessimistic.

But first and foremost, your statement...

"What this means is that even if when you call you automatically win the pot, [button] is still profiting [immediately] if you fold over 30% of the time." (edited for clarity)

...is off- c y?

Oh, btw the 3otb distribution you mentioned was actually {22+, AT+, Axs, KQ-KJ, KTs-K8s, QJ, QTs-Q8s, JTs-J8s, T9s-T8s, 98s} (20.4%), and pertained to a depth of about 40-45bb (and a moderate raise size).