Ask the Slot Expert: A hand I used to misplay in NSU

As I wrote in my column two weeks ago, I don't like giving up a paying hand to take a chance on a better-paying hand. That column was about giving up three-of-a-kind to go for a straight flush when playing NSU.

There's another situation in which I don't really care for the proper play. In this case, however, the worst outcome is ending up with four-of-a-kind and not a non-paying hand.

I played this hand incorrectly the first month or so I played NSU. When I was dealt 2♣ 2♦2♥;7♦8♦, I would be so happy about being dealt a straight flush that I held all the cards. One day something made me check my strategy card. I saw that I had been misplaying this hand.

When dealt a hand with three deuces in NSU, you hold only the deuces unless you have 5-of-a-kind or a Wild Royal.

The following chart shows how the EV of holding the deuces is 14.45513 and the EV of holding the pat Straight Flush is, of course, 10.

For each hand, the chart shows how much it pays (per coin), the number of Ways to get that hand holding the cards at the top of the section, the Total Pays (Ways times Pays), the probability of getting that hand, and how much the hand contributes to the EV.

Even though the probability of getting the deuces is very low, they pay so much more than the other hands that they contribute the lion's share to the EV. I was surprised to see that the Wild Royal is less likely than the deuces.

There are 46 ways to get 4 Deuces. There is one deuce left in the deck and we can replace the remaining discard with any of the 46 cards left in the deck. One times 46 gives us 46 ways.

There are only 40 ways to get a Wild Royal. Each of the four suits has a complete set of honor cards (and tens) in the deck. We need to draw only two of them to get a Wild Royal. Four times the combination of 5 things taken 2 at a time is 4 times 10.

The chart shows that you get a better-paying hand than a Straight Flush only about 15% of the time.

I'm not surprised to see that about 10% of the time you get a Straight Flush. I remember frequently saying to myself that at least got my Straight Flush back after playing this hand.

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