Sunday, November 26, 2006

Stack size and calling an all in when reraised

Lurking in the 2+2 forum archives I found this post I made more than a year ago. Hope you like it and provide some comments about it:

Stack size and calling an all in when reraised (essay). 05/31/05 01:38 AM

This is a usual question in this forum. What is the size of your stack such that you're in desperate mode, or basically commited to call all in when somebody reraise you.

Lets suppose the size of your stack is S = 12x, x = big blind; and you decide to open raise in MP to 4x, and somebody reraise you to 12x, should you call?

The analysis is pretty simple. You need to call 8x for a 18x (12x + 4x and lets suppose there are 2x in the pot to begin with, this varies from 0.5x to 2.5x). So you have odds of 8 to 18 or 1 to 2.25. So basically your hand needs to be 100/(1+2.25) = 30% or better against your opponent range. These are pretty good odds, even with a hand like KJo you're 34% against a range of AA-55, AK-AT, KQ. Even with a AA-88, AK-AQ range, you're 32%, so you need to call.

Now, lets suppose S = 24x, same scenario and you're reraised all in or close to it in practice, like somebody reraised to 20x, you know you're going all in anyway. Now you need to call 20x for a 30x pot, giving you odds of 1:1.5 , now your hand needs to be 100/2.5 = 40% or better; against AA-88,AK-AQ you can not call with KJo, what about AJs? Nope, just 35%. Even AQo is 36.5%, you need better than AQs (39.8%) in this spot vs such range.

Now, lets do the analysis in general for this situation, your stack = S, if you raise to 4x and need to call all in, you need to call S-4 to win a S+6 pot. Then your odds are 1 to (S+6)/(S-4) doing some elementary math, this is 1 + 10/(S-4). With this fraction is easy to see that if you want 1:2 odds, then S=14. Then basically, anytime you're behind the 14x mark, you need to choose a hand to go all in that is just better than 33%.

We can even generalize this result. Instead of raising to 4x, lets suppose you raise to Mx and reraised all in. Now you need to call S - M for a S + M + 2 pot; then your odds are 1 to

(S+M+2)/(S-M) = (S-M+2M+2)/(S-M) = 1 + (2M+2)/(S-M)

Now if you want to get 1:2 odds then (2M+2)/(S-M) = 1

this is 2M+2 = S-M this is M = (S-2)/3 !!! ... (sirio's raising factor )

Then you can manipulate the odds you're getting with your raise (how nice is that!!), if S = 14 then M = 4 is optimal to get 1:2 ; and if your stack = 17x, then M = 5 is the optimal raise to get 1:2 odds.


Tuesday, November 21, 2006

A humility lesson from the Mathematical Olympiad I can use for poker

As you could see by my lack of posting I have not played any poker at all in the last 3 weeks. All my energy has been used in training students for the National Mathematical Olympiad in Mexico and then going to the contest in the city of Zacatecas.
I started teaching at the high school level in 1987 (I was a pretty young high school teacher at 17), I started teaching at the college level since 1992 and I have been involved as a professor in the Olympiad contests since 1991, I've been pretty successful in those since some of my students have won State, National and International contests since then. The Golden age was the period between 1995 and 1997, when the State (Chihuahua) I was responsible for the academic training won the National Contest 3 years in a row, something unheard of at the time. The win in 96 was just monumental, think of the basketball USA dream team in the 92 Olympics in Barcelona, my students were the Mathematics dream team in the country and I was the coach at 26, I felt great and I knew I was making a difference.
Then I discovered poker in 1997, and started to play in my local casino at El Paso, first the 1-3 Holdem and Stud games, 3 months later the 4-8 level and before the year ended I was already playing the biggest game in town, the 15-30 holdem game. I really loved the game and I was good at it, and soon I started to make some money, but of course some other areas in my life suffered because of the insane amount of time I was dedicating to poker. One of these areas was the Olympiad, after winning 3 years in a row, we came in 8th in 1998. I was really disappointed and tried to work harder for the 1999 contest, we made a little come back and placed 3rd that year (out of 32 states). In the 2000's we got 4th,4th,4th,3rd,4th, and 4th in 2005. We still were one of the elite states in the country; but the time I was using to work in the Olympiad was less and less each year, specially after 2003, when I started to play poker in the Internet.
So, 2006 was here, I'm still in charge of the Chihuahua State team, but I didn't work hard enough. I tried to make an heroic effort in the last month, but it was obvious it was not going to be good enough. The Olympiad contest is just too complex to expect a good result without working all year. We went to Zacatecas last week and we came in 18th place out of 32. It was a shameful result. The worst result Chihuahua had since 1991 was 9th; 18th was a nightmare. I felt terrible, I felt I was a total loser and I needed to do something, I'm trying to learn something from this experience. Interestingly enough, there are some similarities between my bad 2006 results in the Olympiad and those in poker. There is the "luck factor"; in the Olympiad, we lost our 3 best students, for different circumstances they couldn't go to the contest, 50% of the team, since 6 students participate from each state, so they have to be replaced with other 3, good, but obviously not as good as them. The luck factor in poker is obvious to all of you who have read (bore ?!) this blog in 2006. But the most important factor is the lack of preparation, the complacency factor. To think, you're so good at poker or Math Olympiad problems, that you'll just keep on winning no matter how lazy you are. I remember in 1994, after coming in 7th in the national contest, I really wanted to win; despite my young age, I developed a plan with the help of some friends to reshape all the things we used to do in the state; we developed a new model to work, and we work hard, really hard, we were really motivated, we had that hunger, we wanted to win it all. The results of all that hard work, came fast, we won 1995,1996 and 1997; our model was even imitated by a lot of states in the country; we were the team to beat in the national contest. But time passed and many states began to work hard, in the meantime we became complacent, we stopped working hard, hell, we stopped working, we didn't improve, we didn't change, and the results are there, many states passed us, they are just better than us now, some of them much better that it hurts. Same with poker, after my monster 2004,2005, I stopped working, I became complacent; too many young kids (and some not that young) with the hunger to win started to work hard and became much better players than me. The Olympiad and poker are some of my loves in my life so far, but I lost that passion, the drive to make you still a better player or coach every day; the complacency state is a terrible one. I need to wake up, I know today what it's my true level in Poker and Math, and I'm not satisfied, 18th place (or barely ahead in poker) is for losers and I'm not a loser, but I'm behaving like one and I need to change.
For the Math Olympiad, I already have great plans to reshape things once again, to innovate, I predict 1st place again in 3 years, and top 3 by 2007.
For Poker, it's a little more difficult to predict results, since in the Math Olympiad you can minimize the luck factor to around zero if you work hard enough, no such thing in poker; but of course you can work hard and play as perfect as you can every hand and they will come.

If you build it, they will come .....