VIDEO POKER

Analyzing a Royal Flush Promotion

Convenience stores are attached to almost every Arco, Chevron, Shell, Texaco, etc. out there. In Las Vegas, these stores regularly contain video poker games with lousy pay schedules. Most good players no longer check pay schedules in these convenience stores because their experience is that these machines "always" offer a poor gamble.

There is one store I know about in greater Las Vegas, however, that has the 100.65% version of Kings or Better Joker Wild for both $1 and $2 denominations. (You'll have to find it on your own. Announcing the location here would kill the games in about 24 hours.) There is no slot club at this store, but you do get free "courtesy cups" should you wish coffee or soda.

Recently this store announced a royal flush promotion. If you hit a natural royal flush in clubs, you get paid double. This makes the game worth about 101.18%, which is quite lucrative if you play for these stakes. Although these are smaller than the stakes I prefer, the potential "dollars per hour" is acceptable --- at least some of the time.

It won't surprise you to know that I attempted to figure out how the appropriate strategy changes for this. To start with, I pulled out "Video Poker for Winners" and set the royal flush to 8,000 coins. I found a number of strategy changes, such as to always hold a 3-card royal over high pairs and two pair. I'll use this strategy on a hand like Ac Qd Jd Qc Jc, where the 8,000-coin royal flush is possible, but from Ad Qc Jc Qd Jd, I'll hold the normal two pair because diamond royals only pay 4,000 coins.

There are a number of such changes, but this article is not about them. The article is to analyze two types of hands where merely setting the royal flush to 8,000 coins won't give you the correct answer. Given this promotion, how would you analyze a hand such as Ah 6h 3h Jc Tc? Under normal conditions you hold the ace, but now the club royal is worth 8,000 coins. This will increase the value of 'JT'. I suggest you work out the procedure before you continue reading. Once you hear the answer it will be obvious, but it's not quite so obvious at the outset. Remember, there is no software out there that allows you to have a different royal flush amount for clubs than it does for, say, spades. You can't assume the problem away by pretending that you have more powerful software than currently exists. You have to make do with the existing software.

The other type of hands that I want you to consider are the 2-card straight flushes with neither flush nor straight penalties. Namely, the hands listed below, where all cards other than the SF2 are totally unsuited with both the SF2 and each other:

In all of these cases, the proper play with a 4,000 royal flush is to hold the 2-card straight flushes. It will be a closer call when the royal sometimes pays 8,000 coins. Why? Because drawing five new cards becomes more valuable. Since these combinations are "bottom of the barrel," compared to drawing five new cards, it is conceivable that the correct play will change for some or all of them. My question is how do we analyze this? Do we use a royal amount of 4,000, 8,000 or something in between? As before, I encourage you to work this out before reading further. The analysis isn't difficult, but neither is it trivially easy. You'll get more out of the exercise is you wallow in it a bit before you read my answer.

Okay. You've had enough time to think about these problems, should you be so inclined. From Ah 6h 3h Jc Tc, you need to analyze the hand twice. First analyze it with a royal flush of 4,000 coins and look at the value of the ace by itself. You should come up with $2.2390 for a 5-coin dollar player. Then you need to analyze the same hand again with the royal set to 8,000 coins and look at the value of 'JT'. You'll see 'JT' is worth $2.0863. This is not a close decision, but realizing that you needed to enter the hand twice is a new concept. If you just used the 8,000-coin royal for both the hearts and clubs, you got the correct play this time but your technique was faulty.

How about the SF2s? What value of royal flush did you use here? On most of these hands, you'll find one, two, or three royal cards. Obviously if any of these were clubs, then any royal you're going to get is worth only 4,000 coins. So the normal play still works. We need to consider the cases where the royal cards that are present aren't clubs.

You might have noticed a number to the right of the hands. This number indicates the number of royal cards in the hand. And since these cards are all unsuited with each other (otherwise we'd hold the 2-card royal), this indicates how many suits you can't get the royal in. (On the low cards, there are some cases where two of the cards are suited with each other. That is, '9T' "23" 4 gives you slightly different numbers than '9T' 234. I'm ignoring this difference in this article. If you wish to consider these cases in your analysis, by all means knock yourself out.)

On the three hands an unsuited QJT is included, do you see that the only suit you can get the royal in is clubs worth $8,000? After all, two paragraphs ago we excluded all cases that had a club royal card. Since this one has the other three suits covered, the only remaining suit must be clubs.

On the hands that have two royal cards, the other two suits must be clubs and one other, for an average of $6,000. On the hands that have one royal card, the other three suits must include clubs ($8,000) and two $4,000 suits for an average of $5,333. Finally, on the one hand that doesn't have any royal cards in it, the average of one $8,000 suit and three $4,000 suits is $5,000.

When I enter in the appropriate size of the royal for each of these three hands, I find that I draw five new cards on three of them: '56' QJ9, '67' QJT, and '9T' 234. The rest of the time I play the normal SF2. All three cases the difference was about a tenth of a cent. Once I knew this, I decided to ignore them and just use the standard strategy. Memorizing three rare exceptions worth so little was too much work for too little gain.

You might question why I spent so much time teaching you how to come with information that I suggested you ignore once you figured it out. To me this article was about "how to figure," not how to use the information once you get it.