Reciprocality: The Cause of Profit at Poker-I

Reciprocality: The Cause of Profit at Poker
Part One
by Tommy Angelo


Before anything flows, there must be a difference. Between different elevations, water flows. Between different pressures, air flows. Between different poker players, money flows.


In the world of reciprocality, it's not what you do that matters most, and it's not what they do. It's both. Reciprocality is any difference between you and your opponents that affects your bottom line. Reciprocality says that when you and your opponents would do the same thing in a given situation, no money moves, and when you do something different, it does.

You can mine for reciprocal gold anywhere in the poker universe. In this four-part series I will examine reciprocality as it applies to information, position, bankroll, quitting, tilt, and betting.

Theoretical money doesn't spend, but it does inspire. I remember when I first heard about it in the form of "expected value." I learned that each wager has two results. There's the expected result, based on analysis, and the actual result, based on events.

I was immediately and appropriately obsessed with theoretical money. All I wanted to know was my score. And I mean I wanted to know it now, as in, right after the hand. But I had no idea how to determine the actual expected value of a street, let alone a whole hand.

Without realizing it at the time, I borrowed from my prior life as a tournament bridge player -- where my score was entirely dependent on the scores of others -- and I came up with a way to analyze a hand of poker that satisfied my need.

After a hand was over, I'd trade places with my opponent. I'd give him my hole cards and my position, and I'd take his, and I'd do a reciprocal analysis. I would imagine how the play of the hand might have gone in the reversed scenario. Then I'd take the imaginary result and I'd compare it to what actually happened, and I'd get a sense of who really won the hand, in theory.

Sometimes I could not figure it out with much accuracy. But sometimes I could, especially if the hand had few variables and branches, and was against familiar opponents.

For example, let's say one day I get pocket kings and Joe gets pocket aces. We play the hand, and Joe wins $100 from me. Right away I'd pretend it had been the other way around, me with the aces, and Joe with the kings. I'd play the streets out and I'd think through the most likely lines and I'd take the resulting probability wave and put a number to it.

In this example, let's say I determined that had I had the pocket aces, I would have won $80. The equation would go like this. Joe won $100 in reality. I won $80 in reversed make-believe. So my final score on the hand is -$20.

Let's hold on to that way of thinking and take a look at starting hands at hold'em. In reality, as we all know, the least profitable starting hand is 72, and the most profitable hand is pocket aces. In reciprocality, the least profitable hand is also 72, but not because 72 is the worst hand. 72 is the least profitable hand in the world of reciprocality because it's the most similarly played hand.

So what is the most profitable hand? Is it pocket aces? Nope. The hand that has the highest reciprocal potential must be a hand that gets played lots of different ways. It's going to be somewhere between the hands that are rarely folded, and the hands that are rarely played. It seems most improbable that it's exactly the same hand for everyone through all time and space, which means the answer will vary from player to player. And that means that any answer we produce is just an educated guess anyway. So what the heck. I'll go first.

The hold'em hand I think I've made the most reciprocal profit on over the years is queen-ten. That's the hand I think I have played most differently from my opponents most often.

So far, I have been answering the question, "What is reciprocality?" In parts two, three, and four of this four-part series, I will answer the questions, "Where do we find it, and how do we cash it in?" by examining reciprocality as it applies to position, information, betting, quitting, bankroll, and tilt. Bring your pick and pan. We'll be mining for gold.