Pot Odds and Implied Odds

[MtnWalker]

A question: From Matthew's new book on Odds and Probabilities p. 64 he states, "For example, an opponent bets $1 and there is $9 in the pot. Your odds are 9 to 1. However, if a player behind you raises, you now must pay an additional $1. A raise lowers your pot odds to only 6 to 1..."

Two questions.

1. Why should a future event, which might or might not occur, be included in the initial decision computation? It seems to me that I would be facing a clearcut, bounded pot-odds situation (9-1) *at the time I made the decision*.

2. Once I decide to bet $1, that particular transaction is over. The pot now owns the dollar, and any future betting decisions I face should rest on the merits, or odds, which exist *when I face the next decision*. In the example, should a raise occur behind me, won't I simply face another distinct $1 betting decision with $12 now in the pot?

I've seen Matthew's point elsewhere. Nevertheless, it seems to me to violate a basic precept, namely, once the money is in the pot it no longer figures into future decisions beyond the resulting increased pot size. I am also bothered by the notion of allowing a hypothetical future event (which I can never accurately evaluate) to determine my present decision when the decision is as major as stay-or-fold. That sounds very much like a guessing game a logical player would rather not engage in, especially in limit hold'em. A similar situation in no-limit carries a whole other level of risk.

Help, please.

[mchilger]

Hi Mtn, this is a good question. In general, you are correct in that the money you've already put into the pot should not impact future decisions. In this particular example, if you call once, you would definitely call again since the odds are even better now.

This concept basically focuses on the importance of position and the value of information. When acting last, you have a great deal of information. You absolutely know that 100% of the time you call you will see the next card for the cost of that call. In these cases, you always know what your pot odds are.

However, if you are not acting last, you are not sure what the cost of your draw is going to be. If you call and no one raises behind you, the cost is $1. If you call and someone raises behind you, the cost is $2. So on average, when you are making the first decision on whether to call or not, you can estimate that your call is going to cost somewhere between $1-$2 (note that sometimes there are reraises so the cost becomes even more). Basically, when you are making your decision, you know that on average the cost will be more than $1 so you need to use this information to make your decision.

Let's use a simple example. You estimate an opponent will raise behind you 50% of the time. In this case, the cost of your draw on average is $1.50 as you need to include the possibility of the raise in your decision. A 50% increase in the cost of drawing might make it a folding decision. Before you make the first call of $1, you have to realize that the cost could be even more so you should include that information in the decision on whether to draw or not.

Whenever I have a borderline decision on whether to draw or not, I will always fold if I look behind me and feel like there is a possibility of a raise.

Hope that helps explain it a little better. If not, feel free to ask another question and maybe some other Members can word it in a better way than I.

Matthew

[MtnWalker]

Thanks Matthew. I guess (hate that word) that I will just have to file this one under "Uncertain Situations" and get on with it.

Your explanation did help. I think part of what has remained unsaid is the fact that this is a decision on a single round of betting, and the conditions bet-call?-[possible raise] could be best compared to bet-raise-call? where in both cases I have to decide whether to stay given a commitment - real (100% probable) or potential (X% probable, where X>0) - that exceeds a single bet..

[mchilger]

yes. I think the key thing to understand is that you can play more hands when acting last than otherwise. If you think of NL, this is especially true since you always have to be worried about someone raising you out of the pot - why call when someone might raise? This is why we often don't limp much in NL before the flop. The same principle applies to Limit when you have borderline draws.

Matthew