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Bob Dancer writes a video poker column for beginners to experts. He also writes a column with Jeffrey Compton, "Player's Edge", featuring information on promotions at various Las Vegas casinos. Player's Edge is published each Friday in the Neon section of the Las Vegas Review-Journal. Click here to send Bob Dancer an e-mail.

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Dec. 18, 2007

Three-Card Royal Flushes in Kings or Better Joker Wild

It's been awhile since I've tackled the 100.65% version of KBJW, i.e. the one that pays 4000 for the royal and 20-7-5 for 4-of-a-kinds, full houses, and flushes respectively. Since this is the showcase game at the El Cortez, where I'll be starting a new semester of classes on January 9, I thought it was time to look at the game again.

In the no-joker section of the strategy, there are ten 3-card royal flushes --- namely 'AKQ', 'AKJ', 'AKT', 'AQJ', 'AQT', 'AJT', 'KQJ', 'KQT', 'KJT', 'QJT'. Some of these have the same value as others, and some do not.

Placing these ten combinations into four unique categories is easy --- so I'll do it myself. Ranking these four categories is tougher. So I'll leave that one for you. As is common in my columns, single quotes will indicate the cards are suited with each other and a W (for wild card) will stand for the joker.

I. Ace and king -- 'AKQ', 'AKJ', 'AKT'
These are the only 3-card royals that include two high cards.

II. Ace and no king -- 'AQJ', 'AQT', 'AJT'

III. King and no ace -- 'KQJ', 'KQT', 'KJT'

IV No high cards -- QJT'

Since this is a "kings or better" game, the ranking is considerably different than what we'll find for a "jacks or better" game. In Double Double Bonus, for example, 'AKQ' is more valuable than 'AKT', simply because pairing the queen gives you your money back. But in KBJW, a pair of queens and a pair of tens are worth the same amount as a final hand, namely zero, so these combinations are all worth the same.

In terms of ranking these four groups, there are some very obvious comparisons. For example, Category I must be more valuable than Category II because pairing the king gives you your money back. Also, Category III must be more valuable than Category II. They each have exactly one high card but the ones in Category III can end up with a KQJT9 straight or straight and the ones in Category II can't. These two comparisons will be valid for every KBJW pay schedule.

The complete ranking, however, isn't so obvious. It depends on the value of the straight flush, flush, and straight and so will be different for different pay schedules. My guess is that no one player in twenty can rank these four categories correctly in KBJW. Can you? Go ahead and try before reading the answer.

Although penalty cards can affect the value of these hands, below is the ranking when the other two cards in the hand are an unsuited three and four. The dollar amounts assume you are playing for dollars, five coins at a time.

Category IV --- Neither ace nor king --- $7.47
Category III --- King but no ace --- $7.40
Category I --- Ace and king --- $7.25
Category II --- Ace but no king --- $6.77

Having 'QJT' in the first position will be quite surprising to several players, as will having Category III higher-ranked than Category I. Straight flushes draws in this game are worth more than they are in most games without wild cards. The $250 straight flushes are worth in this is fairly standard, but the fact that there is a joker in the deck means there are four different ways to end up with a straight flush starting from 'QJT' (W8, W9, 'K9', and '89') as opposed to the two ways you could end up with a straight flush in a game like Double Bonus ('K9' and '89').

Why does this matter? Assuming you wanted a penalty-free strategy, instead of the usual High Pair > RF3 ranking, if you changed your strategy to 'QJT' > High Pair > RF3 with A and/or K, your strategy would improve slightly.

How much of a difference would this make? 'QJT' is greater than AA by 32¢ and greater than KK by 22¢. While these are fairly large amounts, you'll only get one of these hands every 108,000 deals. Multiplying this out it comes out to about a tenth of a cent per hour, depending on your speed of play.

Obviously if this is the only "fine point" you know about the game, it's essentially worthless. If you know dozens or more of these points, most of which are worth more, it makes a sizeable difference. And you need to learn these fine points one at a time, so that's the reason for today's column.

If you're going to learn the perfect strategy (which is usually my goal going in), then knowing the ranking makes it easier to learn.

'QJT', the highest category, is always superior to AA or KK.
King but no ace, the second-highest category, is always superior to AA but is higher than KK only when there is no flush penalty.
Ace and king, the third-highest category, is only superior to AA or KK when there is neither flush penalty nor straight penalty.
Ace and no king, the lowest category, is never superior to AA or KK.
It's easy to see that there are numerous exceptions to the High pair > RF3 penalty-free strategy. Now that we have broken the RF3 hands into four easy-to-differentiate groups, understanding these exceptions is easier.