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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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Oct 17, 2006

AKQJ versus 3-card Straight Flushes

In games without wild cards, the value of 4-card inside straights is determined by the number of high cards in the hand. A high card (usually A, K, Q, and J) are those cards, when paired, give you your money back. When high pairs return $5 and straights return $20, AKQJ, the only inside straight with four high cards, is worth $2.98. Assuming the fifth card doesn't complete the straight or give you a high pair, the rank and suit of that card is irrelevant to the value of AKQJ.

The value of 3-card straight flushes depends mostly on the number of high cards and the number of insides, but the fourth and fifth cards in the hand also frequently change the value of the 3-card straight flush.

In today's column, I want to look at AKQJ and any 3-card straight flushes that can appear in the same five cards. Using quotation marks to indicate suited cards, the only four cases to look at will be AK'QJ9', AK'QJ8', AQ'KJ9', and AJ'KQ9'. The 3-card straight flush 'QJ9' is ALWAYS more valuable than AKQJ, so we're really just going to look at the last three cases.

We do not need to use penalty cards to rank these hands, although to be sure penalty cards affect the ranking.

In 9/6 Jacks or Better, the strategy is:

'KQ9', 'KJ9', 'QJ8'
AKQJ

In 8/5 Bonus Poker and 9/5 Super Bonus Poker, the strategy is

'QJ8'
AKQJ
'KQ9', 'KJ9'

In 8/5 Super Aces Bonus, the strategy is

AKQJ
'KQ9', 'KJ9', 'QJ8'

There are easily-understood reasons why the strategies are different. Once you understand them, if you come across one of these hands in a different game, say 9/5 White Hot Aces, you'll know how to play it. The combinations 'KQ9' and 'KJ9' are always worth the same amount, so I'll arbitrarily select 'KQ9' to talk about.

The combinations 'KQ9' 'and 'QJ8' fit into the category of two high cards and two insides. If the other two cards in the hand are low, eachl of these combinations are worth exactly the same. In the hands 'KQ9'43 and 'QJ8'43, the straight flush combination in both cases is worth $3.21 in 9/6 Jacks or Better, while in 8/5 Bonus both combinations are worth $3.11. The difference in value is because the flush is worth $30 in 9/6 Jacks and only $25 in 8/5 Bonus.

When there are high cards in a hand with these combinations, the value of these combinations become less, and when AKQJ is in the hand, the values of these combinations are no longer the same. With AK'QJ8', for example, in 9/6 Jacks, the value of 'QJ8' is $3.18. The reason this is lower than the $3.21 listed above is that we are throwing away both an A and a K, so ending up with a pair of aces or a pair of kings is less likely.

In the hand AJ'KQ9', the value of 'KQ9' in 9/6 Jacks is worth $3.11, which is 7¢ less in value than the 'QJ8' in the hand AK'QJ8'. While the A and J being thrown away reduce the chances for a high pair exactly the same way as in the previous example, in this case the J also reduces the chances for a QJT98 straight. This 7¢ difference between 'QJ8' and 'KQ9' remains constant in hands containing AKQJ, so long as the straight is worth $20.

Since both $3.18 and $3.11 are greater than the constant $2.98 value of AKQJ, that is why we always go for the straight flush in that game. With what we've already shown, it shouldn't surprise you that the values of 'QJ8' and 'KQ9' are worth $2.98 and $2.91 respectively in 8/5 Bonus, which explains why there is a difference in the plays. ('QJ8' is worth about a half-cent more than AKQJ.)

In 8/5 Super Aces Bonus, the value of the flush is still worth $25. So why isn't the strategy the same in that game as it is in 8/5 Bonus? The answer is that ALL 3-card straight flushes are reduced by 8¢ when two pair gives you $5 instead of $10. Starting from a 3-card straight flush, you end up with two pair 2.5% of the time.

Finally we have 9/5 Super Double Bonus. The flush returns $25 and two pair returns $5, so why isn't the strategy the same as 8/5 Super Aces Bonus? The answer is in this game, the straight flush returns $400 instead of $250. This increases the value of all 3-card straight flushes with two insides by 9¢.

So now we come up to 9/5 White Hot Aces and see that the flush returns $25, two pair returns $5, and the straight flush returns $400, what do you think the strategy would be? Since these values are the same as 9/5 Super Double Bonus, we would expect the strategy to be the same --- and it is.

If we look at 9/5 Triple Bonus Poker Plus, where the pay schedule is exactly the same as 9/5 White Hot Aces except that the straight flush returns $500 instead of $400, what does that tell us about the strategy? Since 'QJ8' is better than AKQJ in White Hot Aces, you know it will also be better in Triple Bonus Poker Plus --- by a larger amount. What you don't know is about 'KQ9'. You might be able to estimate that the 'KQ9' is worth about 6¢ more in Triple Bonus Poker Plus than in White Hot Aces, but whether this makes the value higher than $2.98 or not is not easily determined without a good computer program or an accurate strategy. It works out that 'KQ9' IS better than AKQJ in this game --- by a small amount --- but it's probably something that most players would have to look up.