Defining chances that an ace flops

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Playing hold’em, you have been dealt pocket Kings – a made hand. It’s a big favorite over every other player unless one has A-A in the hole.

Fortunately, that’s a long shot in your favor. Pocket Aces will be dealt to a player only 1 out of 221 hands. With eight opponents at the table, one of them will have A-A only about 1 out of 28 hands. So, preflop, your K-K in the hole is strongly favored to win the pot.

That’s the good part of the story. But, what if the flop brings an Ace? That is a huge scare card! What if an opponent has an Ace in the hole? Fact is an Ace will be dealt to one or more of your eight opponents about 80 percent of the time. (Ref. Texas Hold’em Poker Textbook by Thomas Green; p.159. www.PokerTextbook.info.) Expect an Ace to be out against you.

Now comes the flop: With three cards on the flop, each player sees over 70 percent of his final hand. Holding pocket Kings, you are hoping for a third King. But the odds are about 8-to-1 against catching your set. Likewise, you are hoping an Ace does not fall on the flop. Then an opponent holding an Ace in the hole would have your hand beaten. And, then, you are left with only two lonely outs to win the pot – not a happy situation!

So I asked my poker buddy, Byron Ziman, his opinion. (Byron is a wizard at math and statistics. Years ago, as a student at UC-Berkeley, it was one of his favorite subjects.) How often should we expect to see an Ace on the flop, assuming we know nothing about our opponents’ hole cards? He did a mental calculation, estimating an Ace would flop about 22 percent of the time.

Interestingly, I had conducted an empirical evaluation earlier that evening while playing $4-$8 limit: 14 out of 73 hands had an Ace fall on the flop. That’s a bit over 19 percent; excellent agreement for a small sample size. (Later, when he got home, Byron did a more exact calculation and found that 22.55 percent of the flops would contain at least one Ace.)

What that means to us: Putting it another way, almost 80 percent of the hands dealt will not flop an Ace. Recognizing this, the best way to play your pocket Kings is to raise preflop to thin the field, then keep betting/raising unless an Ace or other scare cards fall on the board. Under these circumstances, chances are your K-K will prevail to the end.

An example: I was dealt pocket Kings in a middle position. After two opponents called to see the flop, I raised. Four of us saw the flop: Q-9-3 with two clubs. It was checked to me, so I bet out, only to be check-raised by the Early-Position.

I knew he was rather aggressive and deceptive. What would you put him on? The highest card on the board was the Queen. Players like to play honor cards. So I figured him for a pair of Queens, but he also could have a draw to a flush or a straight. Less likely, he may have flopped two-pair or a set. All things considered, I decided to re-raise him. Now we were heads-up.

The turn was a red 4 – not likely to have helped his hand. This time he checked to me. I thought about it, and decided to bet for value. Most likely, my K-K was still in the lead. He called.

The river was a red 7. He came out betting. I knew he was somewhat deceptive; he was also low in chips. The pot was fairly big. The pot odds had to favor my calling his bet. He turned up Q-J of clubs. Yes, he did flop a pair of Queens – top pair on the board – plus a draw to the club flush.

Angrily, he slammed his hand down on the table when I showed my pocket Kings and scooped a monster pot.

“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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