Video poker strategy is a balancing act

Video poker strategy can be a bit of a balancing act. A decision that increases your chances of drawing one winning hand decreases, or even eliminates, your chances of drawing others.

That leads us to make decisions based on fine distinctions between pre-draw hands.

One of those fine distinctions led to a note from a reader named Beverly.

"The experts all tell you to discard the ace when dealt three unsuited high cards," she wrote. "Why?"

It's true. In most Jacks or Better-based video poker games, if we're dealt a hand such as A-Q-J-7-4 of mixed suits, the best play is to hold just the queen and jack. But if the deal was K-Q-J-7-4, we'd hold all three high cards.

Regardless of whether you hold K-Q-J or another three high-card combo from among A-K-Q, A-K-J or A-Q-J, you have a better chance at drawing a straight than when you hold two high cards.

And whenever you hold three unpaired cards, you're eliminating some possibilities. With that start, you can't draw four of a kind, and you can't draw a straight flush. There also are fewer three of a kind opportunities, or even chances to draw two pairs, than if you were holding just two cards.

So if we compare A-Q-J and K-Q-J, in both cases we have a better chance of drawing a straight by holding three cards than by holding two, and in both cases holding all three cards means we give up chances at four of a kind and full houses.

So why do we play them different ways? Why do we hold K-Q-J, but just Q-J while discarding an ace?

With K-Q-J we have more chances to draw straights than with A-Q-J, or any other ace-high combination of three high cards. Starting with K-Q-J, it's possible to draw a straight that's either ace-high or king-high, and with hands that already include an ace, the only possible straights are ace-high.

There are 32 possible two-card draws that will turn K-Q-J into a straight, and only 16 that will turn A-Q-J into a straight.

To go into a little more detail on the numbers, dealt K-Q-J-7-4 of mixed suits in 9/6 Jacks or Better, your average return will be 2.58 coins per five coins wagered if you hold K-Q-J. That beats any other possible holds, with the next best being 2.48 coins for holding Q-J.

But if you have an ace instead of a king, you'll get the most value out of holding just queen-jack, with an average return of 2.496 coins per five wagered. The expected value of holding A-Q-J drops to 2.28 coins, lower even than the 2.34 on either A-J or Q-J. Holding two high cards instead of three leaves open the four of a kind and full house long shots, while increasing chances of three of a kind or two pairs. Holding the RIGHT two high cards — Q-J — also leaves open far more straight possibilities.

The numbers are a little different with different pay tables, but we'll discard an ace to hold just two high cards in Jacks or Better, Bonus Poker, Bonus Poker Deluxe Double Bonus Poker — nearly all Jacks or Better-based games.

That greater possibility of a straight with K-Q-J makes it worthwhile to give up any chance of four of a kind or a full house, and to decrease chances at three of a kind or two pair. The lesser straight chances when your three cards include an ace tip the scales the other way, so that we're better off keeping even long-shot chance intact.

It's a question of balance.

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Note that we hold two high cards while discarding an ace in NEARLY all Jacks or Better-based games. There are exceptions in some games with large bonus payoffs on four aces.

Take Double Double Bonus Poker, which pays 2,000 coins for a five-coin wager if four aces are accompanied by a 2, 3 or 4. We still would play A-Q-J-7-4 of mixed suits the same way as detailed above: Hold Q-J, discard everything else, including the ace.

But make the second-high card a king instead, as in A-K-Q-7-4 or A-K-J-7-4, and the dynamic shifts. Then, we don't discard the ace, we discard the other two high cards instead. We hold just the ace.

The bonanza on four aces plus kicker puts a premium on the value of each ace. Even with A-Q-J-7-4, it's a close call, with an expected value of 2.29 coins on Q-J and 2.26 on holding just the A, while holding all three high cards drops a few notches down the list at 2.16. Make it A-K-Q instead, and the value of holding just the A stays at 2.26, but K-Q is worth just 2.21.

The reason is that there are fewer possible straights with K-Q or K-J than with Q-J. With A-Q-J, there are enough other possibilities to give up the long-shot chance at four aces. With A-K-Q or A-K-J, the balance tips the other way.