Most starting-hands are drawing hands. Almost always, they must improve to win the pot.
“Outs” are simply the cards that are needed. But all outs are not alike. How can you best use that information?
You are dealt Ace-Jack of spades and flop two more spades. You now have four-to-the-nut flush. Subtracting those four suited cards from the 13 in the deck at the start leaves 9 more spades that are unseen and (hopefully) available in the deck – waiting for you.
Catch any one of those 9 spades and you have the nut (Ace-high) spade flush. That’s almost certain to win that pot unless someone gets very lucky and makes a full-house. In “pokerese,” we label those remaining 9 spades as your outs.
But wait a second! Another Ace falling on the board would give you top pair, A-A. That too could take the pot. There are 3 more Aces in the deck; so you believe you have 3 more outs.
Well, maybe! There are so many ways an opponent could beat your pair of Aces, assuming you were fortunate (?) to catch another Ace. In fact, that Ace on the board might give an opponent two-pair, Aces-up. Then your hand becomes a poor second-best – a loser, and very likely a costly one at that.
On that basis, those 3 unseen Aces remaining in the deck certainly have much less value than would another spade to make the nut flush. Still, it is possible it would give you the top pair and win the pot against opponents holding a lonely pair – even a pair of Kings.
Being of less value than another spade, I would give each of them 2/3-credit value as an out. On that basis, those 3 Aces, add up to 2 outs (2/3 times 3). Thus, you have a total of (9 + 2) = 11 outs.
The same reasoning applies to your Jack in the hole, but only if no higher card falls on the board (A, K, or Q). Thus, the remaining 3 Jacks are even less valuable as outs than the 3 Aces; so, we give them 1/3 value, for a total of 1 more out (1/3 x 3). Now, you have a total of 12 outs.
With 12 outs, you have a good drawing hand. We can apply the 4-2 Rule to quickly approximate the card odds against making that hand.
With two cards to come (the turn and the river), the probability of making that hand – including the nut-flush, a pair of Aces, or a pair of Jacks – is 12 x 4 = 48%. You can expect to make one of those hands about one-half of the time. The odds are close to even money.
If you want to be more conservative, another option is to not count the 3 Aces and 3 Jacks – just the 9 spades. Then you have a total of 9 outs. Using the 4-2 Rule, the probability of catching one of those hands on the turn or the river, is 36% (9 x 4). Expect to miss about 64% of the time, which makes the card odds about 1.8-to-1 (64% divided by 36%) against you. Now, what?
Look for a PE
Now, to complete our mental gymnastics, estimate the pot odds: the amount of chips in the pot, divided by what it costs you to call to see the turn. Compare this with the card odds.
If the pot odds are higher than the card odds, you have a Positive Expectation; in the long run, you will be ahead by calling the bet. If the pot odds are slightly less than the card odds, consider the implied pot odds, including how many more chips your opponents are likely to put into the pot on the turn and the river. If the implied pot odds are higher, call that bet.
Next issue, we’ll discuss two other cases where all outs are not alike.
“The Engineer,” a noted author and teacher in Greater Los Angeles, is a member of the Seniors Poker Hall of Fame. Contact George at [email protected].