An Interesting Hand in 8/5 ACE$ Bonus Poker

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The cards in ACE$ Bonus Poker (ABP) are just like the ones in regular Bonus Poker (BP) except there are superimposed yellow letters on four cards: “A” on the ace of clubs, “C” on the ace of diamonds, “E” on the ace of hearts, and “$” on the ace of spades. The order of the suits is alphabetical and contract bridge players will also be familiar with this order.

If you get four aces in ACE$ order, either in positions 1-4 or 2-5, you get paid 4,000 coins instead of 400. I’ve written about this game numerous times and have usually said the only changes you make to regular 8/5 BP strategy to play 8/5 ABP perfectly are to break aces full when the aces are in proper sequence for the bonus.

That is, calling the aces by their superimposed letters, from ACE55 or 6A6E$, among many others, you just hold the aces. From AE$44 or KAE$K, also among many others, you’d hold the full house. 

Turns out whenever I said that’s the only change you make to the strategy, I was wrong! (In one article I found one additional hand, A 8 “467”, but I now know there are more than that.) Breaking in-position aces full hands is the only simple adjustment to make, and for more than 99% of players that’s a useful approximation, but there are a number of cases where you holding one in-position ace, sometimes with another card and sometimes not, in ABP and make another hold in BP.  

A friend of mine, Filius Bruce, who’s a very good computer programmer, has come up with a comprehensive list of such cases. His website www.vidpoke.com. He hasn’t published the strategy for this game yet, but it wouldn’t surprise me if he did in the near future.

Let me give you an example. In BP, where suited italicized letters indicate cards suited with each other, as do cards within quote marks, from the hand AQ “89T” you go for the straight flush in BP but hold the AQ in ABP.

Let’s see how common hand that is.

In regular BP, when we don’t care about the position of the cards, this hand arises 12 times out of the 2,598,960 possible combinations. Which in once in 216,580 hands. For reference, that’s three times as often as a dealt royal flush and exactly as often as being dealt aces with a kicker. The way we get 12 times, is the AQ can be any of four suits, and once that suit is selected, the “89T” can be any of the three remaining suits. Four times three equals 12.

In ABP, we start with the same 12 occurrences, but then we have to make adjustments for the position of the ace and the position of the queen. To indicate an ace is in ABP position, I going to underscore it — such as A. For a given suited ace, there can be two positions it can be in. That is, if it’s the ace of clubs, it’s in its proper place if it is either in the first or second position. Similarly, if it’s the ace of hearts, it may be in either the third or fourth position. So that means that only two out of five times will the solitary aces will be in proper position.

Not so obvious until you think about it, the suited queen has to be out of the way in order for the ACE$ to be in order. For example, if the ace of diamonds is in the second position, the queen must be in the fifth so ACE$ may fit into positions 1-4. If the ace of diamonds is in third position, the queen must be in the first so ACE$ may fit into positions 2-5. Once the ace is in position, only one in four times will the queen also be in position.

Since the ace and queen both must be in position for this to work, this will only happen one time in 10 times we have all five cards dealt to us — or one time in 2,165,800 deals. And when it does happen, it’s a pretty close play!

The way I get one in 10 times, is multiplying the 2-in-5 probability the ace is in the correct place by the 1-in-4 probability the queen is in the correct place. There are six different ways the “89T” can be placed in the remaining three spots. All six of these ways are equivalent insofar as the ACE$ bonus goes, so that may be disregarded.

The other hands whose plays are different in ABP than they are in BP are approximately as rare — and as close. It’s fair to say that most of us (including me), don’t want to take the time and energy to remember these rare plays. If we write them down, we will lose far more time storing and looking up the correct play than the correct play is worth!

Nonetheless, it’s an excellent achievement to identify such rare plays even if they are not particularly useful for most players.

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