Ace-High-High Hands in Double Bonus Poker

22 February 2020

By Jerry Stickman

[Most video poker players in today’s casinos use a playing strategy that I call the hunch strategy. They examine the cards that are initially dealt and decide which cards to hold and which to discard based on what they feel is the right move. In other words, they play their hunches.

The hunch strategy can work well in most cases, such as with a hand containing a high pair and nothing else. But it can also get tricky. Video poker players who want to get the most out of every penny played through a machine know that what may feel to be the best hold many times is, indeed, not the best.

This is one in a series of articles that examine some holds that may not look like the best hold, but math proves otherwise. All hands are examined as they relate to several Jacks or Better-based games. Specifically, Jacks or Better, Bonus Poker, Double Bonus Poker, and Double-Double Bonus Poker. And, since pay tables vary from casino to casino (and even within casinos), several popular pay tables are examined.

The term “popular” is taken to mean popular to the more savvy players – not popular with the casino. In other words, only those pay tables that give the player a decent chance to win or at least to play longer. Pay tables that return at least 97 percent to the player if the game has a low variance (meaning lower bankroll fluctuations), and close to 99 percent on pay tables for games that have higher variances.]

The sample hand examined in this article is one that contains an Ace-High-High unsuited. Winpok6 software was used to obtain the results using the specific hand of:

Ace of spade, King of hearts, Jack of diamonds, 2 of diamonds and 8 of clubs. (As Kh Jd 2d 8c).

This hand contains three high cards (As, Kh, Jd) and not much else. Most players using the hunch strategy would save all three high cards hoping for a winning hand containing at least a pair of high cards. But is this the proper hold? By proper, I mean the hold that will return the most money to the player on average.

Let’s look at some specifics.

Double Bonus Poker is a moderate variance game. Many casinos still have this game with decent pay tables paying at least 98 percent. We will specifically look at three Double Bonus pay tables.

The 10/7/5 (10-for-1 for a full house, 7-for-1 for a flush, and 5-for-1 for a straight) version returns 100.17 percent with proper play. While this game can still be found, it is becoming quite scarce.

The 9/7/5 version returns 99.11 percent. This game is relatively common.

The 9/6/5 version returns 97.81 percent and is also common. While not quite a 98 percent return, it is close and many times it is the best that is available. It is also the most commonly available of the “decent” return pay tables.

Now let’s look at some specifics for the 9/6/5 Pay table:

Holding the three high cards (As Kh Jd) returns, on average, 2.2294 credits per the maximum of five credits played.

Holding the Ace along with EITHER the King or the Jack (As Kh or As Jd) returns 2.1832 credits.

In the Jacks or Better or Bonus Poker games, holding the lone Ace was a far inferior hold to any of the above holds. However, because of the added bonus for four Aces in Double Bonus Poker, holding the lone Ace returns 2.1885 credits, on average – more than holding the ace and one of the high cards.

Finally, holding the King and Jack (Kh Jd) returns 2.2479 credits. Holding the King and Jack is the best (and proper) hold. It returns 0.0185 additional credits over holding all three high cards.

The results for the 9/7/5 and the 10/7/5 pay table were very similar to the 9/6/5 pay table, and the order of the preferred holds is identical. Holding all three high cards is the second-best hold, holding the lone Ace is the third-best hold, holding the Ace and one of the high cards was the least profitable hold and holding the two high cards without the Ace was the best hold.

While holding just the two high cards and not the Ace might not seem right, let’s look at why it is.

When the three high cards are held, there are only 1,081 possible hands that can be formed with the cards remaining in the deck. When holding two cards, there are 16,215 possible hands.

When holding two high cards there are two possible results of four-of-a-kind versus zero possibilities when holding the three high cards.

There are 18 full house possibilities when holding two high cards versus zero when holding the three high cards.

There are also more possibilities for all the other winning hands when holding only two high cards versus when holding all three high cards.

That is why the player should hold only two high cards and not all three. But why is holding the King and Jack better than holding the Ace and one of the other high cards?

The number of possible winning hands is identical when holding any of the two high card combinations. Identical, that is, except for possible straights. Because the Ace can only be used and the high end of a straight, there are 112 possible straights when holding the King and Jack versus only 48 when the Ace is one of the two high cards.

As stated previously, holding the lone Ace is better than holding the Ace and one of the other high cards because of the additional bonus for a hand containing four aces. By holding the Ace alone, there are a total of 178,365 resulting hands.

44 are hands containing four aces paying 160-for-1.

Two are hands containing four 2’s, 3’s, or 4’s paying 80-for-1.

Six are hands containing four 5’s through kings paying 50-for-1.

Additionally, a royal flush paying 800-for-1 and a straight flush paying 50-for-1 are possible.

These additional winners combine to make holding the lone Ace the third-best hold.

So, now you know.

The next article in this series will look at the proper holds for this hand when playing Double-Double Bonus Poker.

May all your wins be swift and large and all your losses slow and tiny.

Jerry “Stickman”

Jerry “Stickman” is an expert in craps, blackjack and video poker and advantage slot machine play. 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 stickmanjerry@aol.com