Holding pocket kings, Fred raised pre-flop in a ten-handed hold 'em game. Two others called. After burning a card the dealer placed A-J-2 on the table. "Ace magnets," Fred muttered to himself. Cautiously he bet again. One player folded; the other called.
The dealer placed another ace on the table. Figuring that the second ace made it less likely that his opponent had an ace, Fred led the betting again. His opponent just called.
The dealer placed a third ace on the table. Now convinced that his opponent had started with a jack or two, Fred led the betting confidently. His opponent raised. "She probably doesn't have an ace," Fred thought, "she's bluffing." He called.
Indeed she did have an ace, along with a queen, and smugly stacked a nice pot as Fred fumed. "How could she have an ace," he asked, "when there were three of them on the table?"
"First," I told Fred, "kings aren't ace-magnets. When you hold any two cards that aren't aces, the probability of one or more aces on the flop is 1-C(46,3)/C(50,3), about 22 percent, less than one time in four. We covered that already in the column, 'Ace-Magnets,' in Poker Player, Vol.9, Issue 15, p.14, January 23, 2006."
"Second," I said, "it's true that having aces on the table reduces the likelihood that anyone else will have aces. However, it's not zero. With three aces among the five cards on the table, the odds against an ace among the eighteen cards dealt to your nine opponents are 3-to-2, exactly 60 percent." Fred showed some surprise at that, so I explained that there were 45 unknown cards, of which one was an ace. The probability that the remaining ace would be among the 18 dealt to the others is 18/45, which equals 0.40. In other words it was a 40-60 chance.
So you too will know about aces, the odds that anyone else at the table will have an ace are shown in the table for full and short-handed games. (not shown)
For example, if you and another were the only two left playing at the final table, then the chance that your opponent would have an ace after one fell on the flop is 12 percent. You can also see from the table that with two aces on the tableau, it's more likely than not that someone will have been dealt an ace at a table with eight or more players.
If you're in a tough game, then the players will muck bad aces. If you're in a low-limit game, where no one ever mucks an ace, then you can see from the table that you're likely to be up against paired aces whenever one falls on the tableau, and adjust your tactics accordingly.
"Since she smoothly called you twice," I told Fred, "you should have expected that she had something nice like a good ace or a set of jacks. She can read the board too and she's neither a beginner nor a donkey. I can understand why you led the betting twice, but why did you come out betting on the river?" He didn't answer.
Mr. Burke is the author of Flop: The Art of Winning at Low-Limit Hold 'Em, on sale at amazon.com & kokopellipress.com. E-mail your Hold 'Em questions to richardburke@comcast.net
