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♣.
357 | Value | KQ | Value | |||
| Royal Flush | 4,000 | 0 | 1 | 0.25 | ||
| Wild Royal | 125 | 0 | 34 | 0.26 | ||
| Straight Flush | 50 | 15 | 0.69 | 15 | 0.05 | |
| 4-of-a-kind | 20 | 0 | 62 | 0.08 | ||
| Full House | 20 | 0 | 54 | 0.07 | ||
| Flush | 15 | 63 | 0.87 | 314 | 0.29 | |
| Straight | 10 | 39 | 0.36 | 498 | 0.31 | |
| 3-of-a-kind | 5 | 45 | 0.21 | 1435 | 0.44 | |
| Nothing | 0 | 919 | 13,802 | |||
| $2.14 | $1.74 |
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.
To quote that great philosopher, Yoda: “Do or not do. There is no try”
What I call those two hands is “play them as fast as you can accurately as they are two awful hands in this game.”
I play a lot of NSUD while in Vegas. I love that game because the house edge is tiny but together with the club points it’s a good game all over sudden. During all these sessions I have received my share of Royal Flushes , although sometimes it seems that it’s so hard to get even 4 Deuces. Over the long run, however, it’s a great game. Hopefully Station and Boyd will Keep this game on the Floor without cutting the point value, because this would be end end of NSUD Play for me.
Last time I hit a Royal Flush on a 2outer and was buffled because when I took a Closer look, it turned out to be sequential r-f. There was no extra pay because it was sequential but my host invited me for dinner because I Play a lot, and, from my records, I was still down, despite that Wonderful hand in sequence.
From what I’ve heard, Boyd has already drastically cut the points they give for all VP, especially the games with better returns (like NSUD for example).
The lesson here is: do not play a game unless you have practiced it on computer.
Once again. You CAN NOT get a RF with a 3 5 7 of any suit. If the machine is due, why not help it along and keep the 2 parts of a Royal. All of these machines have an internal accounting program. If they were truly random, it would then mean the Casinos were engaging in gambling. Casinos DON’T gamble. Think about it, what if a poker never gave up a RF ? Or, what if the same machine gave RF away like candy? Nope not gonna happen grasshopper. Both of these situations could occur if the devices were “random”
You need to read “Gamblers Fallacy 101”
I would hate to see your W-L statements.
Mine or Jim’s? If me, I don’t use players cards so it’ll read +$0.00 and -$0.00
The guy who always goes for the RF.
Jim August,
Your logic is flawed and what my father & Grandfather used to tell me. You should have been named Jim December. Then your thinking would be what common knowledge is today.