Pot Odds

People make two kinds mistakes when faced with decisions under uncertainty. Sometimes they stay the course when they really should quit, because they'll lose their investment if they drop out: "In for a penny, in for a pound" as they say. The other is to quit, because the odds say they won't succeed. Don't throw good money after bad."

Both are wrong, as I was reminded while I wrote an email to a poker-playing friend, John Piacente, today.

Ben Affleck playing poker at the annual Ante Up For Africa event in Las Vegas during the World Series of Poker. (Photo credit: Wikipedia)

The starting point for a rational investment strategy is what hey call, in poker, and on Wikipedia,  pot odds.

Pot odds means that you make decisions not on how much you've already wagered, or strictly on how likely it is that you win. Instead, it's a return on investment analysis: what does it cost you to continue (the investment), how much are you going to gain (the pot, not just your money, but all of it) and the odds: how likely are you to win.

Calculating the odds gets tougher the more rounds left to play, and even if all the cards have been dealt, it's still pretty hard. You must first calculate your probability of winning given what you know: your cards, your opponent's face-up cards, and any other cards dealt face up.

Once you make that calculation, you multiply the probability by the size of the pot, and that gives you the expected value of continuing. Compare that with the amount you have to bet or call to stay in the game and you've got what you need for a return on investment decision. But it's not that easy because you're not playing against a deck
, but against another player. And that player has choices to make.

They're going to make the same calculation as you did based on what they know and don't know.  That will tell your opponent whether to stay in or fold. But Your opponent might decide to bluff. In order to deal with that you  have to combine your calculation with your estimate of the probability that your opponent will  bluff.

I remember a night in Hawaii, when I was around twenty, watching a game played by a friend of mine, several other students, and a sailor, whose ship was had come in to Honolulu. The sailor started out losing, and kept losing, a little bit at a time.  He'd ante up, then drop out early, playing very conservatively. That went on until around midnight. Then  he started to win, and the game ended early in the morning, after he'd won everyone else's money.

I found out later that he'd been making his living for years playing poker, and he'd do it the same way: lose small amounts by folding early for two reasons. First, because he wasn't focused on winning he could focus on watching the other players at the table and analyzing their play, looking for ways that they telegraphed a good hand or a bluff, and getting a sense of how often they were likely to bluff. Second, by appearing to be a guy who folded early and never bluffed, he was able to run some big luffs later. Once he knew how the other players played, and once he'd created an illusion about the way that he played, it was easy for him to win.

There's a lot more to poker strategy than that, and there's a lot more to life than poker strategy. But there's got to be an end to this  post, and this is it.

SIDHTN
Should your strategy change depending on how many chips you have?
If your goal is to make money, then you should probably not play unless you know for sure that you are the best player at the table. If you are not the best, then eventually you will lose everything. But you might have other goals. You might enjoy the thrill. Or you might be playing a "training game" with better players to hone your skills.
How do the lessons of poker apply to life?