Am I the Favorite?

The following email was sent to [email protected]. The correct answer, although not that difficult, has too much math for a podcast. So, I’m addressing it here.

I play full pay Jacks or Better (99.54% return), exclusively. I play $1 denomination at max bet for $5 a hand. The casino that I usually play at gives me, at minimum, $90 worth of free play once a week. For cash back, $5 coin-in on video poker earns one point. One thousand points is equal to $1 in value.

Based on this information, do I have an edge? Why or why not? How would I calculate this?

Maybe you have an edge. It depends. Let’s talk about it.

I’m going to assume you play 9/6 Jacks perfectly. That’s a big assumption. It’s probably the easiest video poker game to play perfectly, but most players don’t study and practice enough to play that well. How much your imperfect play costs depends on what mistakes you make. If you go for the royal instead of the flush from A♠ Q♠ T♠ 5♠ J♦, it doesn’t cost you much. It’s a rare hand which costs you very little if you to make that mistake. If you go for the straight instead of the fours in 4♥ 4♣ 5♦ 6♠ 7♥, it’s a much bigger mistake that happens fairly frequently.

The slot club is embarrassingly small. If it really takes $5,000 coin-in to earn $1, that is 0.02%. ($1 / $5,000 = 0.0002 = 0.02%.) Far more common is that $5 earns you five points (which makes it a 0.1% club), but what you present is possible. If it’s 0.1% rather than 0.02%, hopefully you’ll see how that changes the calculation below.

The kicker is the mailer. You told us what you receive, but you didn’t tell us how much you had to play in order to receive that much. How much you have to play is a key part of the equation.

If you play $10,000 coin-in a week and earn $90 in free play, that’s worth 0.9%. ($90/$10,000 = 0.009 = 0.9%.) If you add 0.9% to 99.54% to 0.02%, you have an advantage. If you can play 800 hands per hour ($4,000 coin-in), this edge is worth about $17 per hour.

If you play $20,000 coin-in to earn the $90, that’s worth 0.45%. You now have essentially an even game.

If you play $30,000 coin-in for that same $90, that’s worth 0.30%. Now you’re playing at a disadvantage.

Point multipliers don’t matter much when it’s 0.02% to start with, unless you get something like 25x points, which would be worth a half-percent. Still, even though it’s small, it’s better to play with 3x points than 1x points, although I would play sometimes with the multiplier and sometimes without. Some casinos punish you if they think you only play when the conditions are best. And here, the difference between 1x and 3x is $1.60 per hour, which pales when compared to $90 for a few hours play.

On the other hand, if this casino is 70 miles away and it takes you an hour to drive each way, that should not be ignored. I don’t know what the current accepted figure is for cost of a car including everything, but I’m pretty sure it’s more than $1 per mile. If you’re playing an even game and it costs you $140 in transportation, not to mention several hours, you’re hardly playing with an advantage.

Finally, you said the slot club pays you $90 minimum. That could mean sometimes you get $200. Or some other number. You need to figure out how that compares to how much coin-in you play. It takes a lot of data to figure this out. But it’s not that difficult.

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