In last week’s column, I addressed hands which contained both a Q of one suit and JT7, J97, or J87 of another suit — where the correct play depended on the fifth card in the hand. In today’s column, I will discuss some additional hands in that same game.
Consider a K of one suit and a JT7, J97, or a J87 of another. We know that KJ is considerably less valuable than QJ (because of the number of potential straights), so after last week’s exercise it shouldn’t surprise us that we usually prefer the J-high 3-card straight flush to the KJ.
In the Dancer/Daily strategy for 8/5 Bonus (and also in the Dancer/Daily Winner’s Guide to Jacks or Better), we say these 3-card straight flushes are better with the following caveat:
(< KJ when {JT7 with 8p}, {J97 with 8p} or {J87 with 9p or Tp}). Let’s examine what that means:
With respect to KJT7, assuming you’re a 5-coin dollar player:
If the fifth card is a 2, 3, 4, 5, or 6, JT7 is the better play by 7.3¢
If the fifth card is an 8, KJ is the better play by 0.2¢
If the fifth card is a 9, JT7 is the better play by 1.2¢
If the fifth card is either suited with the JT7, forms any pair, or is an A or Q, the correct play is neither KJ nor JT7.
(If you wish to conclude that it’s more sensible to NEVER play KJ on these hands, because there is only one exception and that is worth 0.2¢, I wouldn’t blame you.)
For K with J97, the only time you hold KJ is when there is an 8 in the hand, and then the KJ is worth 1.2¢ more.
For K with J87, the two exceptions are with a T penalty (making KJ worth 0.2¢ more) or a 9 penalty (making KJ worth 1.2¢ more).
The way I personally remember the differences among these three hands is that I only hold KJ when there is both a straight penalty to the 3-card straight flush AND there’s an 8 in the hand.) The rule covers the situation where there is an 8 penalty and it also covers the case where it’s a J87 and the straight penalty is a 9 or T. If your mind can deal with a compound rule where “8 in the hand” can mean one of two different things, this simplification might work for you also.
Another type of hand begins with KT. In Jacks or Better, with no higher valued combination in the hand, you hold both cards — unless the hand also contains both a flush penalty and a 9 penalty. In Bonus Poker, the flush penalty by itself is sufficient to make the proper play just the K. Assuming there is no A, Q, or J in the hand, holding the K by itself when there’s a flush penalty is worth 2.4¢ more than holding the KT. If there is also a 9 present in the hand, the error from holding KT rather than just the K would be 3.9¢. Players who play 9/6 Jacks or Better strategy perfectly wouldn’t succumb to this last error. However, the players who take the approach that 9/6 Jacks or Better is “close enough” to 8/5 Bonus usually don’t REALLY know Jacks or Better strategy perfectly. And in 9/6 Jacks or Better, most of those players would erroneously hold KT from KT394.
The last group of combinations I want to talk about are 3-card straight flushes with no high cards and no insides — namely 345, 456, 567, 678, 789, and 89T. In 9/6 Jacks or Better, these combinations are ALWAYS superior to AK, AQ, and AJ (collectively called AH in the Dancer/Daily notation). In 8/5 Bonus, these combinations have a lower value because the flush only pays 5-for-1 rather than the 6-for-1 it pays in 9/6 Jacks.
The (slightly simplified) rule is to usually hold these 3-card straight flush combinations in preference to AH except when they have a straight penalty. There are two ways for this to happen.
With 345, every AH combination provides a straight penalty for the 345 because the A interferes with chances for an A2345 straight, so you hold the AH. For 789, the J in AJ provides a straight penalty, so you hold the AJ in that case. Whenever such a straight penalty occurs, holding AH is preferred by 1.2¢.
The reason I said “slightly simplified” is because of the hand AQ “89T”. In this case, the Q definitely is a straight penalty to the 89T, but this is offset somewhat by the fact that the T is also a straight penalty to the AQ. It turns out that you should hold 89T by 0.0003¢ on this hand that occurs once every 216,580 hands. Even to me, this is close enough that it doesn’t matter what you do. I do, however, personally hold 89T when it does happen.
There are other 8/5 Bonus “problem hands” worth discussing. But these last two columns have been too dry for most of my readers so next week I’ll try to pick something that should be of interest of more people.