profitability: pot/implied odds vs. pot equity

[Ludanto]

Let's assume that you play in a game where you can see your opponents' hole cards and they don't know about that (nor will they find out by noticing how well you play). In which case would you make more money long term?

1. You use pot and/or implied odds for your decisions on every street.

2. You calculate your pot equity on the flop and fold or raise until showdown.

3. You calculate your pot equity on every street and decide according to your calculation.

Maybe one or more of those three possibilities will seem ridiculous to you. This might be because I think that I have some screwed up thinking about odds vs. equity sometimes.
Please explain why you choose one of those possibilities or why you would do something else to maximize profit.
There should be a mathematically correct way to play in this game which will maximize your profit because you have all information. I wonder which tools you need to use in which way to make the mathematecally best decisions here.

[kazana]

You can't really pin-point implied odds exactly, because that depends a lot on what villain decides to do. So 1) should be out of the question.

Your pot-equity may be great on the flop, but if you continue to put money into the pot when your pot equity has dropped, then you can't be anywhere close to optimal. So 2) should be suboptimal, too. Unless, of course, you're playing NL and are either pushing or folding on the flop in which case you'll need to hope that villain will always call.

Number 3) looks fairly airtight to me. I'd guess this is as close to optimal as you can get. You can adjust your game to match pot equity as close as possible on every single betting round.

The problem with all three is, is that you need villain to pay you off once you're ahead. This won't always happen, and since you can't know exactly what the maximum amount is villain will be prepared to pay, you can't bet optimally.

[Ludanto]

kazana, thank you for the response. I was also thinking that 3) might be the best of the three ways. Now let's change the game in the way that you don't see the cards of your opponents any more. It is a normal game BUT you have unlimited time for every decision. This means for example you can think about the equities of your opponents and use equity calculation programs. Would 3) still be the best way to go about your decisions? I would assume so. This is why I am wondering if a person have a very good poker strategy even though he/she is not using pot/implied odds at all. Where's the need for pot/implied odds if you had unlimited time on every street?

[kazana]

It's difficult to compare equity with pot odds and implied odds. They are different tools and in an optimal world you'd take all of them into account - actually you should always use all of them.
But I'll still try to point out a few things:

Pot odds play a role when you're trying to justify a call, or trying to deny good odds for any villain to call your bet. So they play a role in folding, calling and betting - all actions available in poker. Needless to say they're immensely important.

Usually, you'll resort to pot odds and implied odds when you believe you're behind.
If you believe you're ahead you should always bet out. Pot odds can help you size the bet correctly.

Equity is a very precise and useful indicator, since it takes hand ranges into account, but take a lot longer to calculate - not to mention that it's virtually impossible (unless you're a mathematical genius) to calculate them without tools.
Also, equity is only your "share" of the current pot, implied value isn't part of it.
In fact, equity is nothing else than your combined outs and the resulting percentage of your chance of winning this hand.

Equity can't tell you how much to bet to deny villain the correct odds to call, either. If your equity is better than your "fair share" of the pot you should be betting. But how much do you need to bet to make it a mistake for villain to call?
If your equity is better than your fair share, any bet is good for you, but you can optimise your expectation by taking pot & implied odds into account.

Equity's use is very limited without pot and/or implied odds. If your equity in a HU match was 49% you should actually fold, because you're behind. Add pot odds to that and you should just about always continue, though.

Gee, this seems to be pretty uncoordinated ramblings, but sit down and think about which decisions you could make with only one of the three tools alone, and you'll get the picture why you actually need all of them for making the best decisions.