Effective Odds vs. Implied Odds

[brianmarc]

In YOP, DS introduces the concepts of Effective Odds and Implied Odds. Can anyone provide a clear, intuitive description of the differences between them, and examples of how they might be used. Are there situations where they migh contradict each other? Has anyone come up with a generalized mathematical expression that incorporates all of the variables DS uses as inputs?

[MarkD]

I think I got a clear example:

Implied Odds
You have a gutshot on the flop and have two opponents and you close the action. It's about 11-1 against you hitting on the turn. The pot is currently offering you 8-1 on your money. Based on pure pot odds you should fold but this would be wrong.

If you call the flop intending to fold on the turn unless you hit then you are in an implied odds situation. If you hit on the turn you can fully expect to make more than number of bets that you were lacking on the flop (11-1 shot only getting 8-1). Thus, the pot is really offering you higher "implied" odds.

Effective Odds
Same example as above - gutshot on the flop. Somewhere you have read it's about 5-1 against you hitting a gutshot on either the turn OR the river so getting 8-1 on the flop you figure it must be correct. If you thought like this your logic would be severely flawed because you have failed to take into account future action.

If you call on the flop expecting to call on the turn as well when you miss then your actual pot odds become 8+2+2 (assuming the 2nd opponent calls the turn bet) to 3 against you. On the flop you were getting 8-1 but effectively you are getting 12-3, or 4-1. Since you are a 5-1 dog in hitting by the river then if you take into account effective odds you can see how the intention of calling the turn when you miss would be wrong.

I'll let someone else clarify any math mistakes - I didn't work out the odds for the example they are from memory and I think they illustrate the concept nicely without worrying about the actual mathmetics.

[brianmarc]

Mark:
Tx for your thoughtful response. Your examples are excellent. My comments:

Follow-up questions: which of the two methods do you use? Here and in other situations? Are there situations when this kind of analysis leads to the Effective Odds method being the correct one? There are probably other ones too, but this is a start as I try to get a complete understanding of the subtleties of these two methods.

[brianmarc]

I've been trying to think through how one would operationallu use these two concepts, and have come up with the following. Use Implied Odds to make the decision as to whether to pay for the turn card. if that misses, use the regular, single-card odds values for deciding whether to pay for the river card. Comments?

[Jezebel]

[ QUOTE ]
Follow-up questions: which of the two methods do you use?

[/ QUOTE ]

You generally want to use implied odds when making a decision on whether to continue in the hand. Mark's example of a gutshot clearly shows why using effective odds is incorrect. Effective odds assume you will be going to the river, which in many cases you will not. Many times you will be correct to see the turn, but fold if you do not improve. If you go by effective odds in these situations you will be incorrectly folding on the flop.

Effective odds are more useful when deciding to call someone down. For instance if you are raised on the turn and are trying to determine if it is worth it to call your opponent down. You know it is going to cost you 2 BB to call down so you compare the total cost vs. total reward and see if the odds are favorable.
You also use effective odds when you are not closing the action. If you are bet into on the flop and have several opponents yet to act, you have to assume that the bet will be raised behind you a certain percentage of the time. So if the pot was laying you 10-1, but you estimate that there is a 50% chance it will be raised behind you, then you are getting 11-1.5 or 7.3-1. The threat of a raise behind you will lower your pot (effective) odds.

[brianmarc]

Jez:

Tx for your insights. You have clarified it nicely. Seems to me, though, that, at least theoretically, there is a false distinction between these two methods. My argument is as follows: If you could calculate the various hand-outcome scenarios, you would always use EO, since IO is really a subset of the possible scenarios incorporated in the IO. But, since it is impossible to in real time to mentally do the kind of math in the complex EO example you provide, we are forced to break the problem into two discrete stages: Use IO to make the flop go/no-go decision. Once the outcome of that decision is known, then make a separate (i.e., discrete) decision on how to act on the turn. By doing this you at least approximate the probabilistic environment in which you are working.

To make the point, consider the following: Assume we had a real-time algorithm that could instantaneously know all the shown cards and parse them for the hand type. Assume also that we know the outs for all these hands as well each time it is our turn to bet, knowing the pot status, number of players in the hand, and number of as-yet uncommitted players to follow us. Assume also our algorithm makes assumptions as to how many players will see the turn and the river, and how many will call in the showdown if we are successful. With all this information our algorithm can then proved an estimate of the expected winnings if we hit, as well as the expected incremental investment that we would lose if we don’t hit. Then compare these two values to get an EV. If >0, accept the bet; if not, fold. The beauty of this methodology is that it can be applied to every post-flop betting situation that requires an EV decision. This include all the standard draws plus back doors and combo hands such as small pocket pair plus backdoor flush. Since we have parsed the hand, we could even adjust the expected winnings for the possibility of hitting the hand but not winning. i.e., for non-nut draws.

Now back to reality: As an exercise to teach myself how to think about these complex issues more clearly, I have designed such an EV calculator in Excel. The over-riding design concept is that we are always looking for reasons to fold, so we use the most conservative assumptions. Preliminary testing indicates that it makes correct decisions. It has also What has also incredibly instructive has been to use it as a sensitivity tool to get order-of-magnitude indications as to what situations are even close to have +EV. Since we are only concerned with the sign and not the absolute magnitude of the EV the approximations this little tool is providing are very useful in real-time situations, providing, for example, insights on how much a raise can destroy your EO, and as a consequence, how many additional callers you would need to your left in order to make the bet potentially profitable. Other tests can be made on how sensitive the decision is to my assumptions on player behavior in subsequent action – for example, one basic assumption is that if the turn is raised, 25% of the uncommitted players will call, while all those with 1 bet already in will also call. Similarly, I assume that the river is always heads up and that if we hit and bet first, our single opponent will always call; but if he bets first there is only a 75% chance he will call us down.

By playing with these values I have been able to get very useful pattern information that, with enough practice, can be internalized to allow for instinctive reactions in real-time.

Since you and MarkD have provided such thoughtful input for me, I’d be more than happy to send you a working copy of this calculator. I’d then be interested in further discussion and possibly development with you. You can reach me nydenizen@yahoo.com.

Cheers!

Brian

[MarkD]

I'm going to read this later because atm I'm tired and in the middle of dishes but Jezebel gave some nice clarifications. I'll give you some quick examples as to when I use EO and IO (EO = effective outs, and IO = implied odds).

You are right, they are essentially the same thing in the sense that they both try to account for some as yet undetermined future action. The distinction is that EO are usually used to refer to situations where the actual pot odds aren't as good as they appear and IO are used in situations where the pot is really giving you better odds then it appears.

So... Preflop I have a small pocket pair in middle position in a loose game. I call. Even though I'm not getting the immediate pot odds to make this hand profitable on this pre-flop round, I know that if I hit a set my implied odds will be great enough to make the pre-flop call profitable.

Another IO example: I close the action on the flop with A5 when the board is (2 5 T). The pot is only giving me 6-1 immediate odds, but I know that if I hit an ace or a five on the turn I expect to make a few big bets by the river so I call.

Effective outs. Same hand as above except this time two opponents act behind me. Now I have to think to myself, "The pot is offering me 6-1, it's 8-1 against me hitting on the turn so if I collect a couple of big bets on the turn then I should call the flop (implied odds). But what if one of my opponents raises behind me? Then I'm not really getting 6-1 on this call, more like 3-1 or 4-1. Now I have to make a lot of bets on the turn and river to make up for the deficit between my draw and the pot odds. Also, there is a chacne that I could make my two pair or trips and still lose. I'll fold and wait for a better opportunity to put my chips in the pot."

So again, I hope this helps. In general I use both and really I don't think about it too much. I did initially, but now it's kind of second nature in most situations. I think implied odds are more useful and really, as far as effective odds go you just need to realize there are situations that the pot isn't as sweet as you might think. Examples are a two flush on board and you have a gutshot. ALthough you are 11-1 against hitting the gutshot you might run into a flush, so in this case I'd want more than 11-1 pot odds to call. This is essentially using the concept of Effective Odds, but I don't quantize the numbers. I come up with general rules where quantization is necessary, like in the above example I'd want 13-1 or 14-1 before I'd call for that gut shot.

[brianmarc]

Mark:

Apologies for delay in repsonding. Again, great insights. I need to absorb all this in my calculator and will sdd to this post in the future if I come across anything interesting to add to your comments.

Cheers.

Brian