Ask the Slot Expert: Which video poker machine should I play to earn a free cruise?

Question: A friend texted me with a question about pay tables on two different cruise ships. As he and I both know, the pay tables on ships are unplayable but he wants to accumulate points toward getting a free cruise (his choice is to play JoB VP over anything else or any other game in the casino). It takes $10 to be played through to earn 1 point and a minimum of 2,500 points for a free low level cruise (as in "Interior Cabin").

He sent me this information about the two ships under consideration:

Ship A: 6/5 25/50 cents - 7/5 $1 - 8/5 $5

Ship B: 6/5 25 cents - 7/5 50 cents - 8/5 $1

He's leaning toward Ship B and 8/5 $1, thinking his money will be put to use the most efficiently toward his points goal. Given these JoB choices, is he correct?

Answer: I've never been on a cruise, so I don't really know what a "low level" cruise is. Only $25,000 in action seems pretty cheap. Does low level mean steerage?

I also don't know what "efficiently" means. In Physics, the Efficiency of a system or process is the ratio of useful energy output to total energy input. I can't think of anything similar for this analysis.

Your friend will have to weigh these aspects:

• The lower the long-term payback of a paytable, the higher the expected loss.
• The higher the denomination, the fewer hands that have to be played.
• The more hands played, the closer the actual loss will tend to be to the expected loss.

The following table summarizes your friend's choices. The first four columns are self-explanatory (LTPB = Long-Term Payback). Expected Loss is the 100%-LTPB times $25,000. Range is my rough (extremely rough) guess about the range your actual loss will fall in.

Playing quarter 6/5 may have the highest Expected Loss, but it also has the narrowest range for actual loss because so many hands are played. If 8/5 is available at dollars, there's no reason to play 7/5 dollars unless Ship A has some advantage over Ship B. I would also rule out $5 8/5 because the risk of a large loss due to a run of bad luck in 1000 hands is too great.

I think I would play the dollar 8/5 too. Staying on ship B, the half-dollar 7/5 is also worth a look. Even though the LTPB is a tad lower than that of 8/5, playing twice as money hands narrows the range. You give up a bit on the upper end of the range, but the lower end is also higher (you may not win as much, but you also may not lose as much). The goal here is to earn the cruise and, although not explicitly stated, earn it without suffering a large loss.

There really is no mathematical sweet spot balancing denomination and paytable. Your friend first has to decide whether he has strong preference for one ship over the other, and then choose a denomination and paytable based on how many hands he's able to play and how much risk he's willing to accept.

Which machine would you play?

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