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Improve your hand to (hopefully) the winning hand. They come in two primary forms: (1) solid outs and (2) tainted outs.

A tainted out is a card that could help your opponent as well as you, possibly giving him the better hand. (Note: In a previous column we ascribed the term, “tainted” outs, as having been originated by poker senior citizen, Byron Ziman of Marina del Rey, Calif. He deserves to be recognized for this intriguing contribution to our poker world.)

The concept is best explained by example: Let’s say you hold A-spades, 8-spades, and flop J-7-4 with two more spades, for a total of four to the nut flush. You have 9 solid outs – the unseen spades (13 – 4 = 9).

In addition, you are inclined to give yourself credit for three more outs to catch another Ace; but these are tainted. If an Ace falls on the board, an opponent holding an Ace with a higher kicker would “out-kick” you, leaving you second-best. That could be very costly! Best to regard the remaining Aces as tainted; we give them only partial value – say, 1/2 in contrast to the 9 spades in the deck/unseen. Thus, our total outs are 9 (the remaining spades) plus 3 x ½ = 1.5, for a total of 10.5.

My Perspective

How about raising after the flop? If an Ace with a higher kicker than your 8 folds to your raise – so now you hold the only Ace in the hole – you have “bought” yourself 1.5 extra outs. And you will have substantially improved your chances of winning this pot.

That’s a big if. An A-K or A-Q won’t fold on the flop to a raise when he holds two overcards to the board. Not likely. More probable, only A-rag (7 or lower) will fold, so your raise really would not eliminate any threatening opposition. You would much rather the A-rag stayed in the pot to help you build it should you connect with the nut flush.

Of course, if another Ace falls on the board, proceed with due caution. Let’s further examine this situation with a little poker math.

If an opponent holds an Ace in the hole, the odds are about even-money as to who has the better kicker. But, what’s the chance he doesn’t hold an Ace in the hole? Accounting for the one Ace you hold, another Ace falls on the turn, so there are only two unaccounted for.

Now, assuming a full table of nine players – 8 opponents, the probability that an opponent holds one of the two remaining Aces is approx. 35% (8 opponents x 2 Aces x 100 divided by 46 unseen cards). As noted above, the probability that his kicker is higher than your 8 is less than 50%. Hence, you are favored in this case. (You would be an underdog if his kicker were higher than yours.) That’s a strong argument against trying to force out opponents when you are fortunate to flop four-to-the-nut (Ace-high) flush.

Can you count Ace for outs? In this example, the tainted Aces preflop gives you about one-half of three solid outs. So we should count these as just 1.5 additional outs – for a total of 10.5 (rather than 12 outs). Should you fail to catch the nut flush on the turn, then, using the 4-2 Rule, your Card Odds are approximately 4-to-1 against.

As long as your Pot Odds are higher than 4-to-1, you should call a bet to see the river. You have a Positive Expectation that will win money for you over the long run.

“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].

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About the Author

George Epstein

A retired engineer, George Epstein is the author of “The Greatest Book of Poker for Winners!” and “Hold’em or Fold’em? – An Algorithm for Making the Key Decision.” He teaches poker courses and conducts a unique Poker Lab at the Claude Pepper Senior Center under the auspices of the City of Los Angeles Dept. of Recreation and Parks and at West Los Angeles College.

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