Caro’s analysis of Irish


Note: Not at the old Poker1 site. A version of this entry was originally published (1993) in Card Player magazine.


Irish hold’em? Let me think. No, I’m not familiar with Irish hold’em, but there are similar forms of hold’em where you’re dealt three or more cards and then discard all but two either after, or before the flop. While novice players instinctively believe they should play more liberally in these games, they actually should not –especially beyond the flop.

The first example given was a hand of A-K-J-8-3 with suits insignificant. The flop was K-K-9. Should you keep A-K (a beginner’s obvious choice) or K-J (the leprechaun’s choice?) Sure, there are good reasons to consider keeping the K-J. If a jack comes on the turn or the river, there’s a chance an opponent will hold the Q-10 combo connecting for a straight at the same time you connect for a full house. How likely is that chance? Not very. Although there’s a much greater chance an opponent will be dealt Q-10 in Irish hold’em than in regular hold’em, the chance that he would keep Q-10 after seeing the K-K-9 flop is small. You would need to assume that an opponent had no playable pair and that the queen and ten were his two highest-ranking cards. Not likely. What typical opponents would invest money to continue playing Q-10 after seeing this flop? If you can correctly make that assumption, save me a seat!

Still thinking out loud… If you keep K-J with the K-K-9 flop and then J-10 or Q-J fill out the board, an opponent could make a straight with just one missing rank, and you could beat it with your K-K-K-J-J. You can even make a rare straight yourself with K-J if the board ends up K-K-9-Q- 10, but it won’t mean as much as you might think, because three kings would be just as powerful against anything an opponent held except another jack.

How Many Jacks Are There, Anyway?

One advantage of keeping K-J is that your king-high full house will devastate an opponent holding J-J when a jack hits the board. But, wait! Let’s count together… two jacks in his hand plus one jack in your hand makes three jacks. Golly, there’s only one jack left among the cards neither one of you has seen. And, in fact, there might be no jack left, because of the remote chance the same opponent started with three jacks and was forced to throw one away. Even if an opponent does have two jacks, the chance of the final jack hitting the board on the last two cards is roughly 1-in-20 And once in a while you’ll even make four kings and beat four jacks. OK, we’re stretching our imagination here, so let’s move on to other possibilities.

What’s bad about keeping A-K? Several things. One disaster is that an opponent might hold A-A and an ace might show up on the last two cards. In that case, you have K-K-K-A-A, which loses to your opponent’s A-A-A-K-K. While not likely, that scenario is more probable than the previous one where you beat an opponent who held two jacks by finishing K K-K J-J vs. J J-J K-K. Why is it more probable? Two main reasons: (1) An opponent is slightly more likely to continue play A-A than J-J; and (2) if an opponent has, say, A-A-J-J-4, he’ll choose to keep the A-A, not the J-J.

Those are just samples of the many paths of logic you must investigate to arrive at the correct card-keeping strategy. But there are a couple very powerful points you should consider. One is that if an opponent hold s A-A and an ace falls, he’s going to win whether you keep A-K or K-J (unless the fourth king falls, also, although you might lose less money with K-J. The best advantages to keeping A-K are that (1) you’ll often split the pot if an opponent also holds A-K, and (2) you’ll often win the whole pot, rather than lose the whole pot, if an opponent holds K-Q. Remember, A-K and K-Q are two of the most common “power” hands your opponents might hold in this situation. When they hold K-9 or 9-9, thus having flopped a full house, it doesn’t much matter whether you keep A-K or K-J.

Poker Engine Analysis

By the way, the odds of your kings-full colliding miserably against aces-full are long. How long? Suppose the ace falls on the river. Well, given the cards you’ve seen (your first five, plus the flop, plus the turn card, plus the river card), the odds against an opponent having had two aces at the time he decided which cards to keep are 85.1-to 1. In fact, the odds against him actually having them at the time the ace hits the board are longer than first because (1) he might have held a starting hand like A-A-Q-9-9 and kept 9-9, or (2) he might have had a king and thrown an ace away.

OK, you’re right. We can’t keep analyzing this forever, because we’re holding up the game. What should we do? Advice: Against typical opponents, the reasons for keeping A-K override the reasons for keeping K-J, so keep the A-K. But it’s not as one-sided as you might think.

Just to be sure, I wrote a computer analysis using something called Mike Caro’s Poker Engine. Seven players, including you, received five cards each. The other six players would check to see if they had any kings or nines. If so, they kept them. If not, they kept their biggest pair, if any. Otherwise they kept their highest two cards. This is not necessarily a perfect strategy, but it isn’t terrible for this kind of hasty analysis. But would they play the hand? I allowed these players to play any pair ranking sixes or higher, any hand that included at least one king or nine, or any hand that contained two cards ranking eight or higher.

Two-way split pots were awarded half a win, three-way splits (playing the board) were awarded a third of a win, and so on. Against this very liberal field of players, here are the results after 150,000 deals (75,000 deals each way, and a total of more than a million individual Irish hold’em hands — seven players per deal:)
If you keep A-K, you win 54.8 percent of the time.
If you keep K-J, you win 53.2 percent of the time.

Looking at the second example, it’s hard to convince the Mad Genius that investing money to keep 7-5 and hoping to hit an inside straight could turn a profit against typical Irish hold’em opponents. The ante would need to be unusually large relative to the amount of the bet to justify this call.

Advice: If you can’t see the turn card for free, pass. — MC

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Mike Caro

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Known as the “Mad Genius of Poker,” Mike Caro is generally regarded as today's foremost authority on poker strategy, psychology, and statistics. He is the founder of Mike Caro University of Poker, Gaming, and Life Strategy (MCU). See full bio → HERE.

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