I enjoy the poker videos that are put out by people like Trooper97 since they show some great sides of Las Vegas. However, a recent video mentioned a Red Rock poker promo that offers $500 for flopped quads on Tuesdays and Saturdays. Some players are going out of their way to play this promotion on those particular nights. Promos like this are usually a terrible value for players and making a schedule of playing them is rarely a good idea. Here’s the probability calculations behind this poker promo.
There is a combination of two probability numbers that we need for this. In order for you to win $500, you have to:
- Be dealt a pocket pair
- Flop quads with that pair
It’s no mistake that I used numbers in the list above. These probability events have to happen in sequential order for you to claim the jackpot. So, while you can assign probabilities to each one of these, you also have to take into account the probability of both events happening. In statistics terms, you need to find the intersection of these two events.
We can use some well-known sources of poker odds and come up with the two probabilities above and write them in proper notation:
Fortunately for us, the math to find the intersection of two probability events is straightforward. We can get the probability of both of these events happening with the following expression:
So you can see that we are left with a final probability of 0.0147% chance of any 1 given hand winning you the $500 jackpot.
A flopped quads promo is a 1-in-6802 hands odds of hitting the jackpot! You would have to play over 20,000 hands to have a 95% probability of hitting the jackpot.
It’s easy to assume that we are going to be able to track our play to 6,802 hands and we should hit the jackpot by then, right? No. We can count on the Geometric Distribution to tell us that if we were to play this many hands, it would give us about a 63.2% chance of hitting the jackpot in exactly 6,802 hands. If you want to give yourself a 95% probability of winning the jackpot, you would need to play over 20,000 hands during the Red Rock poker promo hours.
If we take it down to single hour of play at Red Rock, live poker deals about 30 hands per-hour. The Geometric Distribution tells us that our probability of hitting the Red Rock poker promotion in 30 hands is 0.44%. We can extract that out into an Expected Value (EV) of $2.20 per hour of play. Keep in mind that EV rarely happens to exact degrees in the real world, variance is always going to have an effect on these numbers. If you go out to 20,000 hands, your real world earnings would drop to less than $1 per hour of play¹.
Red Rock Poker Promo: The Conclusion
While these are still slim odds, it’s not the worst poker promotion out there. If you are a recreational player that is just playing a few hours, then this promotion might not mean very much to you; the probability of winning it in a few hours is very small. But if you are (1) a winning poker player and (2) willing to put in a lot of hours during the promo days, then this promotion may indeed add to your hourly win rate for a small potential profit.
¹I realize that I have left the rake, or “jackpot drop”, out of the discussion. Since Stations Casinos handles their jackpot drops a little differently than most, I will be addressing that in a future article.