Ace and Two High Cards in Jacks or Better

1 January 2022

By Jerry Stickman

My wife and I like to play video poker. When video poker-playing friends and relatives from out-of-town visit, we tend to head to our local casino that has excellent Jacks or Better video poker.

My wife and out-of-town friends all tend to use reasoning rather than mathematically generated strategy when they play.

My wife has excellent reasoning when it comes to a vast majority of her decisions playing Jacks or Better. Our friends also do reasonably well with their reasoned guesses.

One place where all of them seem to disagree with the mathematically-produced strategy is a hand containing two unsuited high cards and an ace. Even though the mathematically produced strategy says to save only the two high cards and discard the ace, their logic says to save all three high cards.

They reason that it is better to have three high cards because there is a better chance to get a high pair than when saving just the two high cards.

Do you also follow this logic?

Let’s take a look at a couple of sample hands and see what the math of the game shows.

The stated results are based on a full-pay (9/6 – 9-for-1 for a full house, 6-for-1 for a flush) Jacks or Better game. The results are slightly different for other pay tables, but the best hold is not affected.

First hand: Jc Kd As 4d 7h

My friends would hold the three high cards – jack of clubs, king of diamonds, and ace of spades. Let’s look at the returns from various holds for this hand.

• Holding the three high cards (as my friends do) will return 2.2803 credits for the five credits wagered.
• Holding just the jack returns 2.3066 credits for five – slightly better than holding all three high cards.
• Holding the ace and either the king or jack returns 2.3383 credits – better still.
• Finally, holding the jack and king returns 2.4172 credits. This is the best hold for this hand.

Notice that there are three holds that produce better results than holding the ace and the two high cards.

Let’s try another example: Qd Kd As 4h 8c

In this example the two non-ace high cards are suited. Here are the returns for the top four holds.

• Queen and king – 2.9784.
• Ace and either the queen or king – 2.3383.
• All three high cards – 2.2803.

There you have it. The best return for a hand with an ace and two high cards – with at least one of them unsuited – comes from holding the two high cards without the ace.

The only exception to this rule is if the ace and one (and only one) of the other high cards are of the same suit. You would still save just the two suited high cards regardless of whether one is an ace or not.

You would never hold the ace and the two high cards. In fact, there are three holds that have higher returns.

That’s what the math of the game shows.

As always, may all your wins be swift and large, and your losses be slow and small.

Jerry “Stickman”

Jerry “Stickman” is an expert in craps, blackjack, video poker and advantage slot machine play. He is a regular contributor to top gaming magazines. He authored the video poker section of Everything Casino Poker: Get the Edge at Video Poker, Texas Hold'em, Omaha Hi-Lo, and Pai Gow Poker! You can contact Jerry “Stickman” at stickmanjerryg@gmail.com