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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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April 01, 2008

A Look at Unsuited AQJ in White Hot Aces and Triple Bonus Poker Plus

9/5 White Hot Aces (WHA) (99.57%) and 9/5 Triple Bonus Poker Plus (TBPP) (99.80%) are the very much the same game --- except for the amount you receive for straight flushes. Both are variations on Double Bonus that pay 1199 for four aces, 600 for four 2s-4s, and the "regular" 250 for the other quads. TBPP gives you 500 for a straight flush while WHA "only" gives you 400.

While these are not common games in Las Vegas, there are casinos across the country where one of these is the best game. Without identifying where, I was preparing to play one of these games and was studying the unsuited AQJ hand. Usually you hold the QJ, but when the other two cards are 92, 93, 94, 95, 96, 97, 87, or 86 (with both cards unsuited with the ace), the proper play is to hold the ace by itself. In addition to these hands, if the other two cards are 97 or 96, where the one of these cards (not both) is suited with the ace, the proper play is also to just hold the ace.

It's an interesting exercise to figure out why these particular cases, and no others, form the exceptions to the general rule that you hold QJ. Even if these aren't games you normally play, this will be an educational exercise. The more of these cases you understand, the more able you are to figure out situations that would otherwise be incomprehensible.

When we look at the possible fourth and fifth cards to go along with AQJ, it's easy to exclude the king and ten (as a 4-card inside straight would be held) or the ace, queen, and jack (as a pair would be held). This means we are restricted to those cards lower than a ten --- namely 2-9. There are 32 such cards in the deck. (There are certain combinations within these 32 cards that we're excluding from consideration, such as a 98 --- where the correct play is QJ98 --- and cards that would make a 3-card straight flush with one of the high cards.)

Some these 32 cards hurt the value of the ace. Some hurt the value of the QJ. Some hurt both. Some hurt neither. We need to look at each of these in turn.

Cards that hurt the value of holding the ace by itself ---

1 2, 3, 4, 5 --- These four cards are called "low straight penalties," (lsps) and the presence of any of them adversely affects the chances to end up with an A2345 straight. There are several games where lsps are relevant. In Double Bonus, for example, lsps affect whether you hold either the ace by itself or an unsuited AK, AQ, or AJ. In Double Double Bonus, for example, it can affect whether to hold the ace by itself or a suited 'JT'.

These lsps are not all equal. A 2, 3, or 4 hurts the ace more than the 5 because they eliminate the chance for a specific 600-coin special quad. That is, if you were dealt AQJ93 and held the ace by itself, you couldn't end up with 3333. From AQJ95, on the other hand, you couldn't end up with 5555, but that quad is "only" worth 250 coins, not 600. While this effect isn't relevant in the games we're talking about today, it is in Super Double Bonus and certain other games, so we need to at least have it in our repertoire.

2. Flush penalties --- If you compare the value of AQJ96 where the 9 and 6 are both suited with the queen, the value of the ace in 9/5 TBPP is $2.2766 for the five-coin dollar player. If a 9 or 6 (not both) is suited with the ace, the value drops to $2.2534. If both are suited with the ace, the value drops to $2.2366.

The reason for this drop in value is because it's harder to end up with a flush if there are only ten or eleven flush cards in the remaining pack than if there were twelve.

3. Straight flush penalties --- A suited 2, 3, 4, or 5 hurts the flush chances and ELIMINATES the chance for a straight flush. For the reason cited earlier, a suited 2, 3, or 4 hurts more than a suited 5.

Cards that affect the value of QJ ---

4. The 9 --- The presence of a 9 hurts the chances for both the KQJT9 straight and the QJT98 straight.

5. The 8 --- The presence of an 8 hurts the chances for the QJT98 straight.

6. Flush penalties --- these are not a factor here as the QJ are already unsuited with each other.

Adding it together:

If there are no penalties at all, the hand must be specifically AQJ76, where the 7 and 6 are both unsuited with the ace. All other hands have at least one penalty to the A, the QJ, or both. In most of these cases, we hold the QJ.

The only time we consider holding the ace is if there are straight penalties to the QJ. When we have an 8 (which is the weaker of the two straight penalties), the other card mustn't penalize the ace at all --- hence we have the combinations 87 and 86 only. When we have a 9 penalty, it is strong enough that we can survive one lsp or one fp to the ace --- but not both.

If these were the only games with these types of penalty card rules, I wouldn't waste my time or yours on them. But MOST games with high cards have situations where we have some or all of these same penalties in effect. Learning to deal with them pays dividends in several games.

Finally, doing this article allowed me to discover a really close play. I'm concerned with making minute differences more than most players, but this one was too small even for me.

In the 9-5 version of White Hot Aces, on the hands AQJ97 and AQJ96 --- where either the 9 or 6, not both, is suited with the ace --- the value of holding the ace by itself is $2.252885 and holding the QJ is $2.252852. The difference between these two numbers, $0.000033, means that you have to make the wrong play 300 times before it adds up to 1¢. This is too small for even me to worry about.