Learning Advanced Bonus Poker Deluxe

This is a lightly re-done version of a 10-year-old article. The principles still hold and even if you saw it way back when, we all need refreshers from time to time.

At some denominations and in some casinos, 9/6 Bonus Poker Deluxe (99.64%) can be the best available game. The pay schedule is identical between this game and 9/6 Jacks or Better (99.54%) — save for two items. Two Pair pays 2-for-1 in JoB and 1-for-1 in BPD; 4-of-a-kinds return 25-for-1 in JoB and 80-for-1 in BPD.

A student of mine was competent at JoB and wanted me to help him master some of the fine points at BPD. He already knew the strategy pretty good, but wanted to know it better.

To start with, I asked him to start a hand with a suited ‘JT’ and an off-suit K. I told him to pick four different types of hands where the correct play for JoB and BPD were different. I suggest you try to come up with them before you read on.

My student quickly named these three, using quotation marks to indicate cards that are suited with each other:

He correctly noted that in the first case the suited 5 could have also have been a 2, 3, 4, 6, 7, 8, or 9. In the last two cases, the 5 could have been a 2, 3, 4, 6, or 7. It couldn’t be an 8 because then the play in both games would be JT98.

He thought some more, even consulted his strategy, and then gave up. I told him:

AK ‘JT7’ ‘JT7’ AKJT

In JoB, sometimes you hold the 3-card straight flush with one high card and two insides and sometimes you hold the 4-card straight with three high cards and one inside. In BPD, you always hold the inside straight when you have the choice between these types of combinations.

Notice that in all four of these cases, we held the 4-card inside straight in BPD more frequently than we do in JoB. This is the typical pattern when Two Pair pays 1-for-1 rather than 2-for-1.

Even though he “only” got 75% on this first quiz (How did you do?), he wanted more. Okay. Start from an unsuited AJ. In JoB, you always prefer holding both of them to only one of them. In BPD, sometimes you hold the J by itself. (There are games where you hold the A by itself. In those games, four aces return a lot more than four jacks. That is not the case here.)

My student knew this one — he thought. The relevant penalty cards wouldn’t affect the value of AJ, and clearly the value of the J by itself would be affected by straight, flush, and straight flush penalties. He rattled off flush penalties to the J, as well as an 8 or 9 straight penalty as being the reason to hold AJ. He knew that a 7 penalty wasn’t strong enough to make AJ preferred over the solitary J.

“Almost,” I said, “there is one situation you haven’t mentioned.”

He thought about it and asked whether there was more than one penalty involved.

“Good question,” I replied. “The answer is ‘yes’, and with that answer you should be able to logically infer the correct answer.” 

“We can exclude the king and queen from consideration, because if either of those were in the hand we wouldn’t be considering AJ versus J.”

“Correct,” I responded.

“The 2, 3, 4, 5, and 6 are all “non penalties” to the J, so it can’t have anything to do with them. We’ve already eliminated the flush and straight flush penalties from consideration, along with all 9s and 8s. The only two cards left in the deck are the T and 7, so it must be both of them.”

“Bingo!” I answered. “You’re thinking like a competent player.”

I had one more question to give him. It concerned being dealt a suited ‘KT’ and when you hold the ‘KT’ versus and when you hold the K by itself. In JoB, you needed a flush penalty as well as a 9 penalty in order to prefer the K, and in BPD a flush penalty by itself was sufficient to cause you to hold the K. 

“I know all of that,” he told me, “and I don’t see a question in there.”

“Okay,” I answered, “my question is WHY? Why is there a difference in the penalty card rules between the two games?” This was a question that was beyond mere memorization of the rules.

“I never thought about ‘why?'” he told me. “The fact that the computer said what the correct play was made it good enough for me.” He mused about it for perhaps five minutes and finally gave up.

In both games a flush penalty hurts the value of the K about 6¢ less than it hurts the value of ‘KT’, for the 5-coin dollar player. In BPD, the value of ‘KT’ is only about 5¢ greater than the value of K, so a 6¢ change carries the day. In JoB, the value of ‘KT’ is about 7¢ greater than the value of K, so a 6¢ change makes it a closer play, but the value ‘KT’ is still greater. The 9p hurts the ‘KT’ about 2¢ more than it hurts the K, so both penalties added together are needed to overcome the 7¢ head start the ‘KT’ has.