Ask the Slot Expert: Holding suited ace-10 in NSU

Last week I wrote that you don't hold a suited ace-10 when playing NSU. I use the Wizard of Odds' Intermediate Strategy and it has you always discard the suited ace-10. Maybe another strategy has a situation in which you would hold a suited ace-10.

I checked Bob Dancer's Advanced Strategy for NSU. Bob says that playing his basic strategy returns 99.726% and his advanced strategy returns 99.728% -- an extra dime per hour if you play dollars at 1000 hands per hour, according to Bob. I estimate that you would have to play over 1,000,000,000 hands for this small change in long-term payback to have a greater effect on your results than randomness. The Wizard's intermediate strategy is the same as Bob's basic strategy, so I decided to stick with the Wizard intermediate/Bob basic strategy.

That said, I don't see any instance in Bob's advanced strategy in which you would hold a suited ace-10.

In NSUD, there is EXACTLY ONE instance where you DO hold A,10 suited. It's when the other three cards are EXACTLY 9, 7, 5 of all different suits. An example being A of hearts, 10 of hearts, 9 of clubs, 7 of diamonds, 5 of spades. I learned about this while Greektown in Detroit still had NSUD.

Well, what do you know? Let's check this hand out.

Using the Wizard's Video Poker Hand Analyzer (Note to the Wizard: It's nice that you updated the look of the analyzer, but PLEASE add NSU to the list of predefined paytables!), the EV of holding nothing is 0.317266 and the EV of holding the ace-10 is 0.317484. Sure enough, the EV of holding the ace-10 is 0.000218. If you're playing dollars, that's $0.00109.

Of all the hands you can be dealt, only 24 fit the specified pattern. If you want to try to squeeze every last fraction of a cent out of NSU, you can be on the lookout for these hands. I don't think the return warrants the effort, though. You can read more about this hand at Analyzing Suited Ace and Ten Scenarios in NSU Deuces Wild.

This situation reminds me of a time I was talking with a slot manager in Tunica on The Good Times radio show. We were discussing hit frequency and long-term payback.

I said that players experience hit frequency and the casino experiences long-term payback. Many, if not most, players never play anywhere near enough spins or hands for a better-paying slot or video poker paytable to have a greater effect on their results than randomness.

Last week we looked at why the EV of throwing away the hand is higher than holding the ace-king when dealt A♣ K♣ 3♦ 7♥ 9♠. I almost wrote that the other card with the ace doesn't affect the EVs. I fact-checked this statement before writing it and discovered I was wrong. [Dope slap!] Of course. Some EVs do change when the 2-card royal is ace-king, ace-queen, or ace-jack. I asked you to think about which EVs would change and why.

The following table shows the EVs for holding a 2-card royal and for throwing away the hand for the possible 2-card royal combinations with an ace.

The EV of holding the 2-card royal doesn't change, but the EV of redrawing does. It decreases as the second card in our 2-card royal decreases mainly because we're eliminating more ways we can make a straight or straight flush. When we discarded the king, we got rid of some of the king-high straights. When we discarded the queen, we got rid of some of the queen-high straights and also some of the king-high straights.

For example, when we redraw the hand with the king, there are 1490 ways to make a straight flush. When the hand has the queen, there are 1457 ways. With the jack, 1422 ways and only 1387 ways with the 10.

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