In playing to win, you need to figure out where to spend your time. I came across such a dilemma recently and tried to figure out how to solve it. The problem was too complex for me to solve completely, but I created a simplified model using “reasonable” assumptions and was able to come up with a solution using the simplified model.
Let me explain.
On Wednesday evening, July 3 of this year, Bonnie and I were eating at the South Point with friends. On the way into the restaurant at 5:30, I noticed the jackpot level for the $600,000 “Mad Money Madness” casino-wide progressive was at $23,000. When we finished dinner an hour later, it was at $23,250.
This is a jackpot that will go off before it hits $25,000 (at which time it starts over again at $10,000). If you’re the lucky player who hits it, you get the prize, of course. If you’re playing when somebody else hits it, you get $25 in free play.
It was going up at a rate of $250 per hour, and likely it would go up faster as the evening wore on because evenings generate more slot and video poker players than daytimes do.
Starting at midnight, however, earning double points would begin. This adds 0.30% to the return.
Assume I would commit five hours to play — either before midnight (when the progressive was very likely to hit) or after. Which would have been the play with the higher EV? (Hybrid results of “play until the jackpot goes off and then if you have any more of your five hours left come back after midnight” were not being considered in this model, but might be a reasonable decision in real life.)
The are many combinations of games and denomination I could consider. I’m going to pick two — namely, NSU Deuces Wild for quarters and NSU Deuces Wild for $2.
This game returns 99.728% with perfect play — and for simplification I’m going to assume the return with the normal 0.30% slot club was 100.00% and the return with the double points was 100.30%.
I’m going to assume a speed of 800 hands per hour. This is playing pretty quickly, but nowhere near a record pace. This speed has the advantage of making the coin-in for the quarter game to be $1,000 per hour and the coin-in for the $2 game, $8,000 per hour. Again, round numbers make the math easier.
My next assumption may or may not be valid, and that is a quarter machine and a $2 machine have equal likelihoods of being selected as the winner. This could be true, and it also could be true that the $2 machine has eight times the likelihood because eight times as much is being wagered. The rules are very vague on this. The phrase “any machine any time” could apply to either way of doing it.
I’m also going to assume that in the next five hours, the progressive is going to be hit. Not guaranteed, but very, very likely.
Before I go on, take your best guestimate. Is it worth more to sit down now or wait for double points?
Okay. Figuring out how much the games are worth on double point days is easy. A rate of 100.30% means it’s worth $3 per hour on the quarter machine and $24 per hour on the $2 machine.
Figuring how much the game itself is worth before midnight is also easy. A game worth 100.00% is worth $0 per hour, no matter what your stakes.
So, it comes down to estimating how much the chances at the jackpot are worth. Again, to make the math easy, I’m going to assume 1,000 active players, and that each player has an equal probability of hitting the jackpot. So, on a per-person basis, actually hitting the jackpot is worth $25 — although 999 out of 1,000 people will get zero and one person will have a big smile on his/her face.
We are guaranteed to get $25 when the jackpot goes off so long as we’re playing and we don’t hit the big one. Adding these numbers together, the value of the jackpot to us is $50.
Adding $50 in EV to $0 (the amount the game would be worth with a 0.30% slot club) is also easy. Playing five hours before midnight gives us $50, or $10 per hour.
Comparing the $10 per hour to the $3 or $24 hourly rates we’d earn after midnight is also easy. If we’re playing quarters, sit down and play now. If we’re going to be playing a $2 game, wait for double points.
So, it turns out the problem of whether we should play now or later depends on what denomination we’re playing. I suggest denomination is a consideration that many of you didn’t think was a factor.
The third choice of “the game is not worth enough to bother with” is always an option. Different people will come to different conclusions about that.
If you don’t like my simplifying assumptions, make up your own. Your conclusion will likely end up being the same as mine unless you assume the $2 player had eight times the chances to win the jackpot as the quarter player did. (And I don’t know if that’s a true-to-life assumption or not.) If that’s your assumption, the right conclusion might well be for the $2 player to sit down now and start banging away as fast as he/she could.
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Nice in theory. In reality the positive EV generated by play during the bonus triple point promo is worth what it’s worth because you’re 100% guaranteed to get it. Certainty Equivalent equals Expected Value. CE = EV. In the case of the casino wide jackpot the fact that its $25K or $0 (high variance) means it’s EV of $25 is really overstating the kind of value a typical player should assign to it. CE ≠ EV. In fact CE is more like a fraction of one penny than anywhere close to EV here. For all practical purposes the casino wide jackpot is worthless to the player except purely as entertaining gravy.
How about that fact that you get $25 someone else hits it while you are playing?
That same reasoning is true for any long shot event. Totally dismissing its value would mean you have a zero chance of hitting and that isn’t the case. Variance is high but there is some EV to the play.
You can certainly say it isn’t worth the time or trouble but it does have some value, especially when the jackpot gets close to its ‘must hit by’ value.