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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.

August 19, 2003

Wild Three Card Royals in Joker Wild

Liam W. Daily and I have published a series of strategy cards for a number of video poker games. These cards include four different strategy levels, from Beginner to Advanced, and our advanced strategies are significantly more accurate than any other strategy card published.

That said, it has come to our attention recently via email that we have an error in our Kings or Better Joker Wild card. Although each error pointed out by others is embarrassing, we're actually proud of how few errors have turned up. We were, after all, attempting to publish computer perfect strategy for six different games when all other video poker writers were saying that "perfection" is over-rated. Among other things, this column will correct that error.

Letting a W stand for a joker (wild card), and assume we are talking about suited cards, how would you rank the ten 3-card wild royals: WAK, WAQ, WAJ, WAT, WKQ, WKJ, WKT, WQJ, WQT, and WJT? Obviously two of these cannot appear in the same five cards without there being a paying hand of some sort, so we'll assume the other two cards make up a 3-card consecutive straight flush in the range of W45 W9T, with the caveat that the royal flush combination and the straight flush combination cannot make any paying combination. (That is, we're not talking about W(QT)[98] as that would make a straight).

The ranking of the 3-card royals listed in the following chart. The value listed assumes a suited 56 is in the same hand and you're playing for dollars. Further, my guess is not one player in a hundred even knows the RELATIVE ranking of these combinations --- in other words, prepare to be surprised! And for now, just look at the values in the RF3 column.

	RF3	SF3

WKQ, WKJ, WKT	$10.43	$9.44
WJT	$9.98	$9.58
WAQ, WAJ, WAT	$9.77	$9.44
WAK	$9.77	$9.30
WQJ, WQT	$9.18	$9.58

The fact that the value of a 3-card royal is determined by its highest card is prevalent throughout video poker, so the fact that WAQ and WAJ have equal values shouldn't surprise you any. The fact that WQJ and WQT have equal values is a little bit surprising to players used to pay tables where you get your money back for a pair of jacks or better, but this is a kings or better game so that's not a problem.

The fact that WAK and WAQ have equal values will throw others. After all, WAK has two high cards and WAQ has only one. How can these have equal values? The answer is due to the fact that once you have a joker and one high card, you're already getting your money back --- at least --- for the high pair. Whether the "kicker" is also a high card or not is irrelevant.

The fact that WJT is superior to {WQJ, WQT} (both groups including no high card) and {WKQ, WKJ, WKT} is superior to {WAK, WAQ, WAJ, WAT} (both groups including at least one high card) should likewise not be a surprise. In each case the extra straight flush chances add value.

Further, it shouldn't be a surprise that {WKQ, WKJ, WKT} is the highest ranked category and {WQJ, WQT} is the lowest. After all the first is the more valuable of the two categories where you are guaranteed to get your money back for a high pair and the second is the less valuable of the two categories where you don't have that guarantee.

The surprising part of the ranking, to me anyway, is that WJT is superior to {WAK, WAQ, WAJ, WAT}. The extra chances for straights and straight flushes when you draw to WJT apparently more than make up for the guaranteed win associated with the combinations including WA.

Now look at the SF3 column. It is surprising to many players that the value of W56 can vary so much depending on the other two cards in the hand. The reason for this is the number of high cards still in the pack. When the RF3 contains no high cards, as it true for WQJ, WQT, and WJT, then the value of W56 is the highest because there are still four aces and four kings in the pack to create a high pair. When the RF3 contains exactly one card, as is true for WAQ, WAJ, WAT, WKQ, and WKT, then there are only seven high card still in the pack and the value of W56 is reduced by 14¢. Since WAK has two high cards, leaving only six remaining in the pack, the value of W56 is reduced by another 14¢.

W56 is actually the only 3-card straight flush that has no straight interference with any of the RF3s. W45 is affected more by WAQ than by WKQ, for example, due to the possibility of an A2345 straight. W67 has a different value when paired with WQJ than with WQT due to the possibility of a T9876 straight.

The error on the Dancer / Daily strategy card is that we have all RF3 combinations superior to all SF3 combinations. From the above chart you can see that this isn't true for {WQJ, WQT} when matched with W45 W78. This will be corrected when the strategy card is reprinted.