Pot odds v. Effective Odds v. Implied Odds v. Reverse Implied Odds

[Nemesis]

I understand Pot odds, but the other three seem to run together for me. In what situations should you say hey i'm not getting the pot odds, but i'm getting implied, and when should you say... I'm getting pot, but the reverse implied odds kill me.

[Nemesis]

I guess i should add that i've read and reread the sections on these principles in WLLH, HPFAP, TOP... and i'm still a bit foggy. It seems to me that i always use "implied odds" to chase cards.

[StellarWind]

Suppose there are 10 BB in the pot on the turn and you have the nut flush draw against three opponents. You need to call one bet and no one is left to act behind you.

You are risking 1 bet to win the 10 bets in the pot. Your pot odds are 10-1.

Now if you make your flush you can also hope to win some bets on the river. You don't know how many so you have to guess. Let's say on average you expect to win 2 bets on the river. Your implied odds are 2-1 because you are risking 1 bet now to win 2 bets on the river. Notice I did not mention the bet you will put in the pot on the river. This bet is not at risk because you have the nut flush. You just loaned it to the pot for a moment.

Normally one combines the pot and implied odds: 10 bets in pot + 2 bets on river vs. 1 bet risked now gives 12-1 odds. Those are the odds you should use when deciding to call the turn.

Now suppose that your flush draw is based on 32 and that everyone knows what your hand is. When you make your flush you will not win any bets on the river. Worse, when someone else makes a better flush you will *lose* bets on the river (you have to call in case they bluff). Let's say 10% of the time you make your flush you will lose the hand and lose 1 bet on the river. Your implied odds are 10% * -1 BB = -0.1 BB. These are literally negative implied odds.

Of course you also lose the pot when this happens. I estimate my chance of making the hand in terms out "outs". I have nine outs to a flush but I need to take a 10% discount for the possibility of not winning. Accordingly I estimate that I only have 8.1 effective outs:

Pot odds: 10-1
Implied odds: (-0.1)-1
Total odds: 9.9-1
Outs: 8.1

Of course no one gets this precise in real life, but it illustrates the concepts.

The negative implied odds were small in this example, but they can be large in some cases. Suppose you complete (1/2 SB) the SB with A2o against four opponents. You are getting 9-1 pot odds to do this which is very good. But you will also suffer substantial negative implied odds. This is because you will often make a pair of aces or other marginal hand. These hands will on average tend to lose bets on the flop, turn, and river as you attempt to reach showdown. You get a nice profit out of your pot odds but you could lose it all back and more through negative implied odds. A decision to complete with A2o is an affirmation that you believe the pot odds will outweigh the negative implied odds and leave you with a long-term plus score.

Quiz time: why is it a no-brainer to complete with A2o if it puts you all in?

The term negative implied odds is often used loosely to mean something slightly different. Someone is trying to justify their decision to make a marginal flop call to draw to middle pair, ace kicker. They point to the 9-1 pot odds and five outs and say "no problem". Then a critic comes along and says "bad call, you have negative implied odds." Well that's not literally true. I'd be happy to have the turn and river profits after you successfully make two pair or trips. You will win more than you lose on the turn and river as long as you show a modicum of discretion. Still, the criticism is valid. Two pair will often lose and cost you the whole pot, not just the turn and river losses. When they said "negative implied odds" they really meant "You aren't drawing to a very good hand, you need to substantially discount your outs for the possibility that they won't actually win."

[Nemesis]

Thank you... that's a very good explanation. Exactly what i was looking for. Also you go all in because you're getting to see the showdown for free no matter how much somebody else puts in.


*edit* Lets say you're only on the flop... how do you take into account the bets you "loan" to the pot. If you make your nut flush on the turn then you're good, but if you don't then you have to put in another one bet at least to keep playing. How should you take this into consideration when factoring your outs.