Two Cards or Four? When Does It Matter?  

Consider the following two hands in games where you get your money back for a pair of jacks or better:  A♠ K♠ Q♥ T♦ 5♣ and A♠ K♠ Q♥ T♦ 5♠. There are games where the correct play in both hands is AK; games where the correct play is always AKQT; and games where in the first hand you hold AK and in the second you hold AKQT. Today we’re going to look at which games fall into which category, and why.

First, I’ll provide the “executive summary” for when each condition holds. That’s all some of my readers wish to know. Afterwards, I’ll provide some more detail as to the “why.”

     A. In games where two pair returns 2-for-1, always hold AK.

     B. In games where two pair returns 1-for-1 and straights return 4-for-1, hold AK in the first hand and AKQT in the second.

     C. In games where two pair returns 1-for-1 and straights return 5-for-1, always hold AKQT.

 

Now let’s go a little deeper. In Category A, we basically have Jacks or Better and Bonus Poker. The pay schedule matters not at all for the value of AKQT, so long as it has the standard return for straights, two pair, and high pairs. The value of AKQT is always going to be $2.66 for the five-coin dollar player.

The value of AK, however, is also affected by the value you get for full houses and flushes — but not much. Holding AK in 9/6 Jacks or Better is worth $2.87 and $2.79 and in 8/5 Bonus Poker these values drop to $2.82 and $2.75 — which are still well above the $2.66 benchmark for holding AKQT. A key fact that will come in later in the article is that in the Jacks or Better case, when the low card is unsuited with the AK, then AK is worth 21¢ more than AKQT, and when the low card is suited with the AK, then AK is worth 13¢ more than AKQT.

You do get a full house holding AK one time in 900 and flushes one time in 99 when the fifth card is unsuited with the AK and one time in 136 when the fifth card IS of the same suit as the AK. These are not big numbers. The pay schedules matter, but unless you get into a Bonus Poker game that is so bad that two pair only returns 1-for-1, you always prefer AK.

How much you get for two pair doesn’t affect the value of AKQT because the only hands you can get when you hold those five cards are a straight or a high pair. From AK, however, you end up with two pair every 22.8 times. Since that means an extra $5 every 22.8 times when you get one unit more, changing the value of two pair from 2-for-1 to 1-for-1 is worth 22¢.

Close readers might remember that in 9/6 Jacks or Better when the low card was unsuited, AK was only worth 21¢ more than AKQT, so why wouldn’t changing the value of two pair change the play? The answer is that in the games where two pair receives 1-for-1, the value of 4-of-a-kinds (especially aces) is much higher than the $125 you get in Jacks or Better. Even though you only only have a 1-in-16,215 chance to get four aces holding AK and drawing three cards, the difference in the payout from $125 to $800 is worth about 4¢.

In 9/6 Double Double Bonus, for example, holding AK is better in the first hand by 4¢ and AKQT is better in the second hand by about 4.5¢. To me, these numbers are plenty big enough that I’m going to pay attention to the suit of the small card in these hands. Whether they are big enough for you to reach the same conclusion is a decision you’re going to have to make for yourself.

The third category where two pair returns 1-for-1 and straights return 5-for-1 is really just the best versions of Double Bonus Poker. Since the straights pay 25% more than they do in most otherwise similar video poker games, it should be no surprise that you hold AKQT on both hands.

There are a few games that will not fit these rules exactly, and variations on games like Ultimate X, but in general these rules apply widely.

I picked AK in this case. I could easily have chosen AQ or AJ with exactly the same results. All three combinations are equal.

The rules for KQ, KJ, and QJ are different than the ones given here. Perhaps I’ll discuss them in another blog someday.