It’s Not About Trying

I was teaching an NSU Deuces Wild (the 16-10-4-4-3 version that returns 99.73% with perfect play), and was discussing the hand 3♥ 5♥ 7♥ K♣ Q♣. The correct play, by a mile, is to hold the hearts. One player raised his hand and said: 

“But just what are you trying to get holding the hearts? You’re mainly going to get low-valued hands and the highest possibility is only worth $50. Why don’t you go for the KQ and try for a $4,000 royal flush? It doesn’t happen very often, I realize, but the possibility is there and when you hit it, you feel good!”

Good question! The math is basically impossible to figure out mentally, but it’s easy for a computer. A key factor many players ignore when they do a seat-of-the-pants calculation is that there are 15 times as many possibilities when you’re drawing three cards (specifically 16,215) than there are when you’re drawing two cards (1,081).

To determine the value of each possible draw, you multiple the frequency of how often it happens times the value when it does, and divide by the number of possible draws. Below I’ve done that for you. I’ve left out four deuces and 5-of-a-kind from my chart because neither of those hands is possible when you hold either 3♥ 5♥ 7♥ or K♣ Q♣.

The chart presumes you are playing for dollars, five coins at a time. I’ve rounded off the numbers to pennies. For our purposes, it’s close enough. There are a number of interesting numbers in the chart. The correct play doesn’t change if you’re playing for any other stake. It’s just that if you’re playing for quarters, for examples, all amounts are divided by four.

First, let’s take the holding the hearts. About 1/3 of the total value of the combination ($2.14) comes from ending up with a straight flush (69¢), and the rest is spread out among the lowest three pay schedule categories. 

When you hold the clubs, ending up with a royal flush is worth about 25¢ (you have a 1-in-16,215 chance to get $4,000), and the ending values of a wild royal, a flush, a straight, and 3-of-a-kind are all worth more than that! 

The key numbers to me are the totals, namely $2.14 if you hold the hearts and $1.74 if you hold the clubs. I would make the correct play even if it were less than a penny’s worth of value. Four 40 cents, it’s a complete no-brainer. Even if my intuition told me that going for the royal flush was better, I’m a strong believer in the math and will hold the hearts every time in this hand.

Also interesting is I’m not particularly trying to get any hand! My concentration is on playing the hand correctly rather than what hand I end up with. If it’s a one-card draw, to A♦ K♦ Q♦ J♦, for example, then I suppose you could say I’m trying for the royal flush. Although any number of people have told me they “never” connect on one-card draws, it happens frequently enough (1-in-47 draws) that I still get a little excited when I get such a draw and am disappointed a bit when I miss.

But on a hand drawing two or more cards, there are way too many possibilities to count. I’m just playing the game as accurately as I can and accepting the results. When I get a royal, my normal comment (if somebody else is around) is “I guess it’s my turn.” When I do not get a royal, usually I say nothing and keep on playing. 

I do know players who live and die on their results on every hand, but that’s not me. I’m too busy playing the next hand to worry about what I did or didn’t get on the last hand.