# The peculiar power of Caro’s Conception

Note: Not at the old Poker1 site. Originally published (2006) in Bluff magazine.

Twenty-five years ago, I published a concept that had already changed the way I plotted and planned poker strategy. I called it Caro’s Conception.

It began innocently, by simply showing that you could give an opponent first choice among three groups of exposed draw-poker hands. There were nine hands in each group. After your opponent’s choice was made, you could take second choice among the two groups remaining. Then you could use a random method to decide which hands were shown down against each other. And you’d always be the favorite, assuming you chose the correct remaining group, even though you’d had second choice of hands.

Of course, luck played a part, and if you only randomly chose hands a few times, you might lose. But the power of probability took a firmer and firmer grip the more times you played. So, if you gambled for thousands of showdown hands, you were almost sure to win. Then I showed an even simpler example. Each group – hearts, clubs, and diamonds – contained only three cards. You give your opponent first choice of suit and you choose second. Then you randomly match up one card from his suit and one from yours. High card wins. You’re the favorite, even though you didn’t get first choice.

Show me the cards

Are you having trouble believing me? Well, here are the groups of cards…

K♥ J♥ 6♥

A♣ 9♣ 7♣

Q♦ 10♦ 8♦

There are nine possible match-ups for any two competing suit-groups – three cards from the first group versus three from the second, so 3 x 3 = 9. If your opponent picks hearts, then you pick clubs and you’ll have a 5-to-4 edge. If clubs are chosen, pick diamonds, and you’ll also have a 5-to-4 edge.

So, it would seem that clubs are better than hearts and diamonds are better than clubs. That makes diamonds the best choice, right? What if your opponent chooses them? Well, if your opponent chooses diamonds, then you simply choose those lowly hearts. They have a 5-to-4 edge against the diamonds! You see, no matter what your opponent chooses, you’re the favorite.

Now, while this is interesting, it isn’t the point. But before we move on, let’s have a little more fun. Players have adapted this concept to hold ’em, which wasn’t widely popular when I first defined Caro’s Conception. It’s time for you to choose a hold ’em hand. After you do, I’ll choose from the remaining ones and we’ll deal out cards forever – or until you get tired of losing. Pick a hand…

Hand A: 10♥ 9♥

Hand B:  2♣ 2♦

Hand C:  A♠ K♥

 If you choose A If you choose B If you choose C … and I choose A (not available) 54% win rate* 40% win rate … and I choose B 46% win rate (not available) 53% win rate* … and I choose C 60% win rate* 47% win rate (not available)

The asterisks above indicate what I should choose.

Strangely, no matter which hand you choose, you’ll take the worst of it. And here’s where Caro’s Conception gets weirder. It states: In poker and in life, traits, tactics, and interactions can be ideally suited for success against specific opponents while failing against other opponents  – even weaker ones.