Calling all in before the flop in NL

In an earlier post, I lost a buyin in NL hold'em when I called an all in bet preflop with Ad Kc against Qh 4h. At the time I felt that it was acceptable to risk a part of my bankroll to get my money in as a favorite.

An interesting question is how much of my bankroll should I be willing to risk in such a situation. To simplify things with this example I'm in the BB with Ad Kc. It folds to villian in the SB who brazenly shows me his Qh 4h and moves all in. He has me covered. The hand is in isolation so assume no metagame considerations. Also assume no rake. What should I do?

Obviously going all in with AKo against Q4s is a profitable play. If you're not comfortable putting your stack in as a big favorite then you should be playing limit or not playing poker. How much of a favorite am I here? I used PokerStove to determine that Ad Kc is a 63% favorite over Qh 4h all in preflop.

So how much of my bankroll should I be willing to risk in this sitation which is profitable but has a risk of losing. The Kelly Criterion provides the formula.

f = (bp - q)/b

where:

* f is the fraction of the current bankroll to wager;
* b is the odds received on the wager;
* p is the probability of winning;
* q is the probability of losing, which is 1 - p.

In this case the all in is even money so b = 1 and the formula reduces to

f = p - q

In practice many people divide f by 2 and use that. This reduces variance while still realizing most of the expected profit.

So in this case as a 63% favorite, I could risk up to 13% of my bankroll using the conservative value of f.

f = .63 - .37
f = .26
f/2 = .13


A related question is if I put 5% of my bankroll in play at a NL table, what kind of favorite do I need to be to call all in preflop for my stack at even money. This is important to an NL cash player because the standard guideline is to not put more than 5% of your bankroll in play at one table.

Using the equation we set f = 0.05 and solve for p.

0.05 = p - q
0.05 = p - (1 - p)
0.05 = 2p - 1
1.05 = 2p
p = 0.525


That's a pretty slim edge. In practice the player will need a larger advantage than this to allow for rake. Because of rake, b is actually less than 1. So I'd probably want upwards of p = 0.6, a 3-2 favorite, to put a buy in on the line.