I have talked a lot about the importance of math in poker decisions. The math can be fairly simple (if I call that bet, how many chips will I have left?) On the other extreme, there is a section of Harrington on Holdem where the author uses seven pages of math to solve a poker problem.
A lot of the poker math nerds hang out in the Poker Theory thread on the twoplustwo.com poker forums. I want to get better at my decisions late in tournaments, and I want to advance beyond a general understanding of the concepts, and really dig down, work the math,and study it deeply.
This is cutting-edge poker theory, in fact, the concept of Bubble Factor has only been around for a year or two as far as I know. That makes it a timely topic for this post. For those who want to know more there is a link at the end of this post.
Here is the question that I posted:
How are ICM and Bubble Factor related? I'm starting to dig more deeply into the math of poker and I've never seriously studied either, though I've done some reading about Bubble Factor.
I would like to dig a little more into these concepts, but I don't quite understand how and if they are related to each other. From what I know they both seem to be about considering tournament and prize pool structures when considering a bet, for example, the bubble factor would obviously be very high if you're in a satellite that pays the top ten the same amount, 15 players are left and you're in third place.
Are they two ways of saying the same thing? Is one more important than the other in different situations?
Here is the best response that I received:
The bubble factor (BF) is Prize $ lost if you lose the hand / Prize $ gained if you win. It uses ICM theory to get these values. It is easy to show that it is always greater than 1.0.
Assume an all-in bet of B when the pot odds are P. Then in a cash game the required equity is B/(B+P). Dividing numerator and denominator by B, you have
eq_chip >= 1 / (1+Pot Odds).
For a tournament, your winnings -- the chips in the pot, translate to P/BF dollars in prize money, the metric you’re really interested in. Substituting this for P leads to the needed equity under ICM of
eq_icm >= 1/(1+Pot Odds/BF)
Example:
With a pot sized all-in bet of 10, the pot is increased to 20 and your pot odds are 2 to 1; you need 33% chip equity for +cEV in a cash game. For a tournament, if your bubble factor was 1.4, you need for +$EV
eq_icm = 1/(1+2/1.4) = 41.2%.
Assume an all-in bet of B when the pot odds are P. Then in a cash game the required equity is B/(B+P). Dividing numerator and denominator by B, you have
eq_chip >= 1 / (1+Pot Odds).
For a tournament, your winnings -- the chips in the pot, translate to P/BF dollars in prize money, the metric you’re really interested in. Substituting this for P leads to the needed equity under ICM of
eq_icm >= 1/(1+Pot Odds/BF)
Example:
With a pot sized all-in bet of 10, the pot is increased to 20 and your pot odds are 2 to 1; you need 33% chip equity for +cEV in a cash game. For a tournament, if your bubble factor was 1.4, you need for +$EV
eq_icm = 1/(1+2/1.4) = 41.2%.
A reasonable question to ask is why do you need more equity in a tournament; everyone has the same issue? The answer is that EV is relative; you should always be comparing against alternatives. Here, for an all in bet the alternative is folding. In a cash game folding has zero cEV when the baseline stack size is that at the decision point. However, for a tournament, folding ALWAYS has positive $EV. Therefore calling requires a higher portion of the pot to do better than folding, which translates to higher required equity.
http://dokearney.blogspot.com/2009/05/theory-posticmbubble-factor-part-2.html
No comments:
Post a Comment