In Poker, Take Odds on the Pot; Don't Marry It

Pablo sketches what he says are children dancing around a dove. If Pablo's surname is Picasso, Southeby's sells it for millions. If Pablo's last name is something else, his mom hangs it on the refrigerator with a magnet next to the Joe's Funeral Home calendar. To most folks, the pictures seem interchangeable. But one's worth megabucks and the other space on the ice box.

Bobby is playing seven-card stud poker. He has A-S J-S in the hole and 10-H, 7-S, 4-S, and 2-Cexposed. Four players are in the pot. An exposed 8-C, 6-H, 2-D, 8-Sbets the minimum. Two hands fold. Bobby calls. If we're discussing poker champ Bobby Baldwin, calling is shrewd even if it bombs. If the Bobby is a typical low-limit casino poker plodder, the wager may be artless even if it wins. The casual kibitzer thinks the bets are comparable. But one has a positive expectation and the other negative.

What's the difference in the poker situation? The sophisticated bettor makes the decision based on "pot odds." The less skilled solid citizen marries the pot.

The good player reasons along the following lines:

1) The pot is at $75. A $5 call means I'm risking $5 to make $75. The payout is 15-to-1.
2) The betting pattern of the player with the eights suggests he may have two pairs but not triplets.
3) I'm practically sure to win with a flush if I draw a spade. I'll most likely lose with a high pair.
4) I've seen 22 cards, mine in the hole as well as all live and folded up-cards. These have included seven spades.
5) I therefore have six ways to draw a spade from the unknown 30 cards, so the odds against a flush are 24-to-6 or 4-to-1.
6) Say I called with this hand five times. Statistically, I'd lose four times - $20. I'd win once - $75. My expectation is a profit of $55 over five bets, $11 for each $5 bet.

The weak player has no idea what cards have been exposed and mucked. He hasn't studied his opponents' habits or watched the betting. So he doesn't know his chance of a flush and hasn't a clue whether the hand with the eights is apt to have two pairs or triplets and therefore in a position to draw a full house on the end. His reasoning is pretty much as follows:
1) I've sunk $25 in this pot so far; it'll only cost me $5 more to protect my investment.
2) I can beat the eights with an ace, jack, 10, or any spade.
3) This game is mainly luck. Everyone's pulled it out on the end and you can't do that by folding. I'm here to gamble, not watch. And, I need big pots like this to get back even.

Sure, it's tricky to figure pot odds for some draws. In stud, especially, it takes remembering what's been exposed and mucked as well as checking what's on the table.

Pot odds are easier to figure in hold'em than stud because fewer cards are exposed and they're always in sight. But, more cards are unknown so odds against successful draws are steeper. For instance, assume a stud player goes to the river with two pairs, needing a full house to beat an apparent flush, and neither match has been among 28 known cards. The player can use four out of 24 unknowns - so the odds are 20-to-4 or 5-to-1; the pot would only have to exceed $50 for a $10 bet to be attractive. In hold 'em, a player would see just six cards before the river and would therefore be looking for four out of the remaining 46. Odds are now 42-to-4 or 10.5-to-1. The pot for a $10 bet would have to be at least $105 for this to have positive expectation.

So much for why betting on the come makes sense for one Bobby and not the other. What about one Pablo's sketch being worth more than the other's look-alike? Maybe that's best addressed by analogy with Sumner A Ingmark's rationale distinguishing his immortal poetry from rhymes written on Madison Ave to sell soap.

A master with respect is treated,
'Cause his great deeds are oft repeated,
While lucky ducks are soon defeated.