# Big Sequential Royal Jackpot

Recently, at the Red Rock Resort in Las Vegas, a lucky quarter video poker player, with a \$1.25 bet, collected more than \$150,000 for a sequential royal flush.

I’ve received a number of inquiries asking things such as: Was I said lucky player? (no) Was it a play with a positive expectation? (yes) and, If I had known about how large the jackpot had grown, would I have been playing it? (absolutely not!)

Let’s look at it more closely.

One out of 60 royal flushes is sequential. At 800 hands per hour, it takes 50 hours for each royal, so that’s 3,000 hours for one sequential royal flush cycle. That’s about one and one-half years

of 40-hour weeks.

Yes, you could hit it today, or go 10,000 hours of play without hitting it, but on average it’s 3,000 hours. The binomial distribution, which I wrote about a few months ago, tells you how to figure out things like the chance of hitting it in “only” 1,000 hours.

The game itself at Red Rock is 6/5 Bonus Poker, a game that returns 96.9%. At the same 800 hands per hour rate (which is conveniently \$1,000 coin-in for that hour), it will cost you \$31 per hour on average to play that game. For each of your 40-hour weeks, that’ll cost you more than \$1,200 on average, or more than \$60,000 a year. While this gets offset somewhat by slot club benefits (customers willing to lose \$60,000 a year are very valuable and casinos treat them well), for most of us this will get very old very quickly.

To be sure, if the royal came like clockwork after one and one-half, you would have lost \$90,000, but a \$150,000 jackpot would make you whole again. And then some. Even after taxes. But this jackpot has likely been building for a lot longer than one and one-half years. If you hit it and only won \$50,000, you’d still be way behind.

And what if it took two or three cycles to hit? What if you were down that much and some other evil player hit the jackpot? That kind of loss is way more than most quarter players can afford.

The actual play on the jackpot hand was a no-brainer. According to the picture in the paper, the cards ended up being, in order, AKQJT, with the queen being the only card drawn. That play would have been made by anybody sensible, no matter what the actual center card was.

There are other interesting hands where you can play aggressively for the sequential, which will shorten the cycle somewhat, but also increase your average loss rate.

Take the hand, in order, A♥ K♥ Q♥ Q♠ 9♦, when the sequential royal jackpot is at \$120,000. The normal play in 6/5 Bonus Poker is to hold the queens. But with a sequential jackpot this high, it seems obvious to hold the hearts. Right?

Let’s find out. If you hold AKQ, you’ll end up with a royal flush every 1,081 times on average. Half of the time, that royal will be \$1,000 (and look like AKQTJ), and half the time, it’s the sequential worth \$120,000. So, on average, a royal from this position is worth \$60,500 (242,000 coins). Put that into any video poker software, and you’ll see that holding the hearts is worth 227 coins while holding the queens is worth a measly 7.5 coins. It’s correct by a mile to hold the hearts.

Let’s look at a 3-card draw, say 4♣ 5♣ 6♣ J♣ T♣. Do you throw the 456 away (a dealt flush worth \$6.25) and go for a \$120,000 sequential royal? Actually, the question I want to ask is, “Are you supposed to keep two cards or five?” I don’t really want to know what kind of gambler you are. I want to know what kind of disciplined mathematician you are.

If you hold the JT, you have a 1-in-16,215 chance at a royal. Those royal draws could be AKQ (\$120,000), AQK (\$1,000), KAQ (\$1,000), KQA (\$1,000), QAK (\$1,000), or QKA (\$1,000). Tell me you wouldn’t be disappointed to only collect a \$1,000 royal and I’m tempted to call you a liar!

So, over all six royals, you’d collect \$125,000, worth, on average, \$20,833, or 83,333 coins. You’ll see the flush is worth 25 coins and holding the JT is only worth 17. Did you get that right?

How about a suited JT in position along with trip fives? Still correct to hold 555, but it’s kind of close. At \$150,000, it would be correct to hold JT.

Here’s an interesting one. Assume you’re dealt, in this specific order, 2♥ 4♠ Q♦ J♣ 3♥ when the sequential is at \$150,000. While the normal play when the royal pays \$1,000 is QJ, you’ve decided, right or wrong, to hold one of the high cards because they’re both in sequential order. But which one? Try to figure it out on your own. The answer is at the bottom.

There is no software out there that I know about that allows you to change the value of a sequential and it figures out the stuff for you. So, you have to do it yourself.

Are you willing to do this considerable amount of work to create your own strategy for a game that will cost you more than \$1,200 a week on average?

Me neither.

Even though it’s a game with a positive expectation, you have to be the one to hit that royal in order not to lose a fortune along the way.

I don’t know how many machines were tied to that sequential. If there was only one such machine, theoretically you and two buddies could have each taken eight-hour shifts for 18 months. If this went according to average (Big if!), you would each have \$30,000 in losses in the year and a half before you collected \$50,000 each. (Not including your fourth partner called Uncle Sam).

Good luck with finding partners willing to do that and actually sticking it out for a long, expensive, time.

And if there were more than one such machine, having enough players to tie up all the machines for such an expensive play would basically be impossible. In addition to being unprofitable.

Answer to question: Holding the queen is much better than holding the jack, in spite of the jack having more straight and straight flush possibilities. Why? Simply because the queen is part of TWO sequential royals: AKQJT and TJQKA.