The promotion I’m going to talk about today happened several years ago and I may be off on some of the details. For the sake of this column, assume the details are as I present them. The purpose of this column is to explain how to evaluate and play a promotion that might come up in the future, rather than describe exactly one that has come and gone a while back.

The promotion was at a casino in California, and the best game for dollars at this casino was 9/6 Bonus Poker Deluxe (although many players played Double Double Bonus or some other game.) The BPD game is like Jacks or Better, except all quads pay 400 and two pair just gives you your money back. This game returns 99.64%, the slot club paid 0.25%, and there were mailers of $200 four times a month (almost weekly, but not quite) if you played at least $300,000 coin-in over the previous three months. Players who played this much also received free rooms and meals. On occasion there were other promotions as well — in addition to multiple other casinos relatively nearby.

  If the player played exactly $100,000 in a month, the mailers were worth 0.8%. If you played twice that much, the mailers were worth 0.4%.

The promotion required you to get all 13 quads, and when you did, you received an extra $500. And then you could immediately start on your next 13 quads. To find out how much this is worth percentage-wise requires a bit of calculation. As a first approximation, I’m going to assume all quads are equally likely to occur — at a rate of one quad per 428 hands. Using this approximation, let’s see how many hands it takes to get each of the 13 quads.

I used Excel. I figured it would take 428 hands to get the first quad. The second one would be 428*13/12 = 464 because only 12 of the ranks would count towards getting all 13. The third one would be 428*13/11 = 506 because now there are only 11 “new” quads. When we get down to the 13^th quad, the formula becomes 428*13/1 = 5,464 — which is how many hands on average it’s going to take to get the last one. We add these all up and we get 17,694 hands. If this takes you 20 hours, this is a $25 per hour addition to an already positive game ($500/20 hours = $25 per hour).

  At $5 per hand, 17,694 hands will cost you $88,470 coin-in during which time you should have hit 41 quads (most of which duplicated a quad you have already claimed). Since 41 quads are worth an extra $500, this means that each quad, on average is worth 400 + 500/41 = $412 (approximately). Putting this into WinPoker or some other video poker program will tell you the game is worth 100.2% — plus the slot club, plus the mailers, plus whatever other promos they decided to run at the same time. You can figure it out more precisely, if you like, but this was close enough for me to understand what was going on.

This was a nice promotion. It takes 5+ hours each way to drive there from Las Vegas. I was told about it at the time and decided I didn’t want to drive that far at least twice a month. It might be worth more than $30 per hour when I’m there, but it kills more than ten hours round trip each time I go and there are car expenses to consider.

One lady, “Joyce,” who regularly made the trip posed the following question to me: Let’s say I had all of the quads completed except kings. I was dealt KK443. How do I play the hand?

In normal 9/6 BPD, the correct play is to hold both pairs. In the way Joyce set up the problem, when you collect four kings, you get $900 instead of the normal $400. If you always collected $900 instead of $400 for a quad, the correct play would be just to hold the kings. So, this time, what do I do? A group of friends were there, including “Dave,” who is probably more knowledgeable about video poker than I am. He traveled from Las Vegas to Southern California because he was no longer welcome as a player in most-or-all Las Vegas casinos.

Before I reveal my answer, what would you do? Would you just hold the kings, or would you hold both pairs?

I told her that I would hold both pairs. And from KKK44, I’d hold all five cards.

“Yes!” exclaimed Dave. “That’s what I told you! Now that he tells you the same thing, Joyce, how will you play that hand?” 

“I’ll just hold the kings, whether from two pair or full house. Whatever you two so-called experts say, holding the kings makes more sense to me.”

It’s a $0.72 error to try for the kings from two pair (where you have about a 1/360 chance to connect) and more than $11 when you hold KKK rather than a full house (where you have 2/47 chances to connect). The 100.20% figure assumes you are going to use the same strategy all the way through. 

Joyce seems to be confusing getting the 13 quads more quickly rather than making the most money.

It was a lucrative enough promotion that Joyce was still a favorite even with these “misplays” (depending on how well she played the rest of the hands). But it was a more lucrative play for Dave, who didn’t make these unforced errors.