A version of this article first appeared in 1999, but I haven’t written about it for a long time and many of my readers are newer to the game than that and didn’t see it the first time.
In 9/6 Jacks or Better, if you start from A♥ K♣ Q♦ J♦ plus another “nothing special” card, it is a close decision whether to hold AKQJ or just the ‘QJ’. Breakeven Point (BP) analysis is useful in determining what to play. The following analysis assumes you are playing for dollars. If you are playing for any other denomination, then consider the numbers presented to be “coins”, rather than “dollars.” For example, a royal flush is $4,000 for dollars, but 4,000 quarters, or 4,000 nickels or 4,000 $5 tokens if that’s the denomination of the machine you are playing.
The BP tells the dollar amount of the royal flush where the value of QJ equals the value of AKQJ. Notice that as the amount of the royal flush increases, the value of ‘QJ’ increases and the value of AKQJ stays the same. When the BP is less than $4,000, you should hold ‘QJ’. When the BP is above $4,000, you should hold AKQJ.
Assuming that the fifth card is not an A, K, Q, or J (which would give us a high pair), or a T (which would give us a straight), or the 9♦ or 8♦ (which would give us a type of 3-card straight flush which is higher in value than either AKQJ or ‘QJ’), the actual card can fall into four separate categories. The completely accurate rules for each of these categories are as follows:
Category 1: Fifth card is a 9. Three cases (i.e. 9♠, 9♥ and 9♣). Hold AKQJ. BP=$4,185
Category 2: Fifth card is an 8. Three cases. Hold ‘QJ’. BP=$3,945.
Category 3: Fifth card is lower than an 8 and is not a diamond. Eighteen cases. Hold ‘QJ’. BP= $3,624.
Category 4: Fifth card is lower than an 8 and is a diamond. Six cases. Hold AKQJ. BP=$4,975.
HOW to calculate these figures is an article for another day. Many people do not want to vary their strategy depending upon the final card. In truth, if you always play ‘QJ’, the biggest error you ever make is for 6¢ (Category 4 hands) and it doesn’t happen very often. If you always play AKQJ, the biggest error is for 2.3¢ (Category 3 hands). This error also doesn’t happen very often, but it does happen three times as often as the other kind of error.
Let’s assume for now you are taking a “penalty cards are more trouble than they are worth” attitude. You want to ALWAYS hold ‘QJ’, or ALWAYS hold AKQJ on these hands. But you’d like to know WHICH ONE IS BETTER?
It turns out that the answer is “it depends.” The preferred type of weighted BP for these hands is $3,982. Since this value is under $4,000, the conclusion seems to be “hold ‘QJ’ on average”. And there is really no debate on this among video poker writers — before now. Every author who gives an “advanced strategy” somehow distinguishes the correct play for each of the four categories above, and when these same authors provide a “simplified strategy” they all say hold ‘QJ’.
What isn’t being considered, however, is ARE YOU GOING TO LEAVE A TIP? When you hit a $4,000 royal flush, do you leave a $20 tip? Many people leave this much or more. (This is equivalent to a $5 tip for a quarter player on a $1,000 jackpot, should it lock up, or a $100 tip for a $5 player on a $20,000 jackpot.) If you do, then AKQJ is the play that returns the most, not ‘QJ’. Tipping $20 means that the royal actually returns only $3,980. Since the BP is above this, namely $3,982, AKQJ is now preferred.
Liam W. Daily and I struggled with this when we created our strategy cards. The Advanced Strategy was clear, because we identify the correct plays for all four categories, but what about our Beginner, Recreational and Basic strategies? Do we assume the people using our cards are “cheapskates” and hence advise ‘QJ’? Or do we assume the people using our cards are “typical tippers” and hence advise AKQJ?
We decided to provide the “cheapskate” strategies (i.e. advise ‘QJ’), but to write articles like this one informing players of the types of hands where their tipping practices can affect the proper play. This week I am discussing such a play for 9/6 Jacks. Down the road a bit, I’ll indicate where tipping practices affect plays in other games too.