Friday, August 30, 2013

Poker: Pot Odds 2

Some follow up thoughts on the first post about odds. To get the most precise numbers for your hand's equity/odds, you should compare pot odds with your hand's odds of hitting its outs.

So using the same scenario from the first post, the third/most precise method is as follows:

Method 3 == Pot Odds vs Odds of Hitting Outs
Pot odds == 1:5
Your hand has 8 outs. On the turn, there is 52 - 5 = 47 cards left. Your odds of hitting  outs is 8 : (47-8) == 8:39 == 1:4.875
Since pot odds > odds of hitting outs, you should call.

So note that this is much more precise, and only deals with the turn card (ie. if you had read the second post about bet sizing, this assumes that you will bet optimally on the turn again and that effective stack size is large enough for optimal bet)

However, the disadvantage of pot odds is that when the probability is small, the odds change very rapidly to any small change in probability. ie. 1:49 vs 1:99 is actually only 1% apart. So whereas for equity calculation, you are "safe" if you have say a 5% buffer between required equity vs hand equity, here there is no similar rule and you might be easily mislead as to how much edge you have.

Let's look at what a 5% equity edge means for different pot odds.

Bet SizePot OddsRequired # of Turn Outs Without BufferEquity + 5% BufferRequired Hand Odds With BufferRequired # of Turn Outs With Buffer
1/4x pot1:57.821.7%1:3.610.2
1/2x pot1:311.830.0%1:2.314.2
1x pot1:215.738.3%1:1.618.1
2x pot1:1.518.845%1:1.221.4

Without the 5% buffer, the Required Hand Odds should equal pot odds. Instead, as you can see, 1:5 -> 1:3.6, while 1:1.5 -> 1:1.2. Hence there is no easy way to build in some buffer with pot odds. However, you may have noticed that the required outs actually increases by a constant (2.4 outs) when you build in a 5% buffer. This makes perfect sense- 2.4 outs --> an extra 5% chance of drawing out.

Thus the optimal way to give yourself a buffer is to calculate the odds as is, but then require a couple extra outs to be conservative.

Interestingly, if you look at the # of outs required for 1x pot and 2x pot bets on the flop, they are actually "ahead" (> 50% chance of drawing out by the river). So it seems as though any drawing hand that could call a > pot sized bet could also just raise or push all-in. More on this next.

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