10-14-2005, 07:46 AM
Unnecessarily Complicating Pot Odds: Part 1
This all started back in a post a few days ago where I made a flop call with an underpair and was heavily berated for it. It really made me question just how much I really knew about pot odds and how the maths behind the psychology really work.
Basically in this series im trying to put some numbers to the natural instincts most players develop over time. Recently Ive noticed that pot odds are something that I know I, and im sure many others, use often without really considering all the factors that go in to making decisions regarding them. It’s fairly experimental, and to be honest im not sure what the results will show at the end, but im definitely going to enjoy the journey.
First lets try to simplify things as much as possible just so we can get the basics down:
The game is dry holdem. Whats ‘dry holdem’? Its holdem without the river (har har). Basically the game plays as follows. You get two cards, there is a SB round of betting, the flop is dealt, another round of SB betting, and then a turn with a BB round of betting. Best 5 card hand is shown and takes the pot.
Your situation in this game is as follows, you hold a hand which has X outs to improve. If you hit any of these outs, you will take down the pot. Without hitting one of these you are guaranteed to lose the hand. Furthermore you have the worst poker face in the history of poker. If you hit one of your outs, your opponents are guaranteed to check/call the turn against you to minimise their loss to 1 bb each.
Lets also assume there is a lot of pride involved in this game, and there is zero chance you are going to get either player to fold at any stage, and this is a fact known by all players. And lets also assume that X isn’t a big enough number for you to have the equity to make a value raise profitable. Your choices at all stages in the hand are call or fold.
The preflop raising has left you with a pot of exactly J bb and 3 runners; A, hero and B. One of these players is in front of you, the other is behind.
Player A is the BB. Player B is sitting in MP2 and was the PFR. Hero (you) is sitting in MP1.
Player A in front of you bets….. time to go in to the tank and think this one out.
What are your immediate odds here? Lets see, your paying .5BB for a J + .5 pot?
J+.5 : .5
2J+1 : 1
But this isn’t the case at all, not in this hand, not even for this street. Why? Because there is a player to act behind you, and they still have options too.
If Player B is just going to call as well, then the numbers are still easy.
Now your paying .5BB for a J+1 pot.
J+1 : .5
2(J+1) : 1
The implied odds for when you hit are pretty easy too, because the pot is only gonna give you another 2 bb, and they are guaranteed.
J+3 : .5
2(J+3) : 1
So, still assuming player B will call as well, lets see what you need for the play to be +ev.
X outs means you will hit your hand 2X% of the time with one card to come (assume also that this is perfectly exact).
So, 2X% translates in to….
100/(2X) – 1 : 1
Now the ratios are the same, we can work it out, for +ev:
2(J+3) must be bigger than 100/(2X) – 1.
So we call when:
2J+6 > 50/X – 1
J+3.5 > 25/X
For example, lets say the pot was 2 bb on the flop and you had 5 outs (typical 2 pair/trip outs).
5.5 > 5
Yep. You have .5 of an advantage here. Its +ev. So of course you must call. But how much needed to be assumed to get to even this stage?
Coming in part 2:
What if Player B messes your whole plan up and raises? And what if Player A decides to fight back and 3 bet? What if Player B has the nuts right now and caps? Suddenly that .5 blows all the way out to 2. And of course once committed you can hardly fold right? The pride would kill you….. =P
This all started back in a post a few days ago where I made a flop call with an underpair and was heavily berated for it. It really made me question just how much I really knew about pot odds and how the maths behind the psychology really work.
Basically in this series im trying to put some numbers to the natural instincts most players develop over time. Recently Ive noticed that pot odds are something that I know I, and im sure many others, use often without really considering all the factors that go in to making decisions regarding them. It’s fairly experimental, and to be honest im not sure what the results will show at the end, but im definitely going to enjoy the journey.
First lets try to simplify things as much as possible just so we can get the basics down:
The game is dry holdem. Whats ‘dry holdem’? Its holdem without the river (har har). Basically the game plays as follows. You get two cards, there is a SB round of betting, the flop is dealt, another round of SB betting, and then a turn with a BB round of betting. Best 5 card hand is shown and takes the pot.
Your situation in this game is as follows, you hold a hand which has X outs to improve. If you hit any of these outs, you will take down the pot. Without hitting one of these you are guaranteed to lose the hand. Furthermore you have the worst poker face in the history of poker. If you hit one of your outs, your opponents are guaranteed to check/call the turn against you to minimise their loss to 1 bb each.
Lets also assume there is a lot of pride involved in this game, and there is zero chance you are going to get either player to fold at any stage, and this is a fact known by all players. And lets also assume that X isn’t a big enough number for you to have the equity to make a value raise profitable. Your choices at all stages in the hand are call or fold.
The preflop raising has left you with a pot of exactly J bb and 3 runners; A, hero and B. One of these players is in front of you, the other is behind.
Player A is the BB. Player B is sitting in MP2 and was the PFR. Hero (you) is sitting in MP1.
Player A in front of you bets….. time to go in to the tank and think this one out.
What are your immediate odds here? Lets see, your paying .5BB for a J + .5 pot?
J+.5 : .5
2J+1 : 1
But this isn’t the case at all, not in this hand, not even for this street. Why? Because there is a player to act behind you, and they still have options too.
If Player B is just going to call as well, then the numbers are still easy.
Now your paying .5BB for a J+1 pot.
J+1 : .5
2(J+1) : 1
The implied odds for when you hit are pretty easy too, because the pot is only gonna give you another 2 bb, and they are guaranteed.
J+3 : .5
2(J+3) : 1
So, still assuming player B will call as well, lets see what you need for the play to be +ev.
X outs means you will hit your hand 2X% of the time with one card to come (assume also that this is perfectly exact).
So, 2X% translates in to….
100/(2X) – 1 : 1
Now the ratios are the same, we can work it out, for +ev:
2(J+3) must be bigger than 100/(2X) – 1.
So we call when:
2J+6 > 50/X – 1
J+3.5 > 25/X
For example, lets say the pot was 2 bb on the flop and you had 5 outs (typical 2 pair/trip outs).
5.5 > 5
Yep. You have .5 of an advantage here. Its +ev. So of course you must call. But how much needed to be assumed to get to even this stage?
Coming in part 2:
What if Player B messes your whole plan up and raises? And what if Player A decides to fight back and 3 bet? What if Player B has the nuts right now and caps? Suddenly that .5 blows all the way out to 2. And of course once committed you can hardly fold right? The pride would kill you….. =P