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.
I’ve enjoyed my fair share of dealt royals. And, I’ve been fortunate to hit 2 royals after tossing all five dealt cards. However, as much as I find it unlikely, I’ve never hit a sequential (or reverse sequential) royal. I’m somewhat obsessive in recording my play results, and note the sequence of every royal (limited 50/100 play excepted).
What I value most in my play is that results typically converge on a positive outcome in relatively short order (say, with a very strong probability over any given 2 or 3 year period). For similar reasons noted by Bob, investing in an exceptionally reliably negative drain for the promise of a jackpot possibility that some other player might drain, with no equivalent play opportunity in sight, is keenly off my radar. Any adverse play results essentially end up being a sunk cost when the opportunity vanishes, rather than conceived as variance (as is the case when the play is one of many reflecting loosely comparable risks/rewards)..
A side note that I forgot the other day. I had a razgu (toss ’em all, hit draw) royal last year at a Vegas casino. The bullet screwed it up, as the hand was KQAJT. Even funnier was that it was on an NSUD game. Also in my last post, I will wager that a huge % of folks that chase the seq. will be doin’ a lot of Mr. Reed’s B side song!
Fascinating lesson in mathematics, logic and greed! Thanks Bob
I’ve been playing VP since the late 70’s when it was invented. I have pretty much alalyzed every worthwile game at 1 point or another. After all that, variance calcs., bankroll req.,what if’s this and that, you can always go to the Jerry Reed method. This country boy rapper has been gone for 12 years, but he summed this strategy in his 1971 hit single–which was “When you’re Hot, You’re Hot”. Also part of the other part of the lyric is “when you’re not, you’re not”. I am sure the old scratched up single is packed in my attic. For those who want to hear and see it, is is on Youtube. As a psyic side note, the B side of the single was “You’ve Been Cryin”.
Nudge
Nudge, your comment gave me a good chuckle. Jerry Reed was a favorite singer, songwriter and actor of mine. The “Jerry Reed Method” is how I play when playing non-advantage games like craps for fun.
My guess is that Red Rock eliminated another bank of jackpot and merged the amounts together. I have watched this specific bank with a progressive for the sequential (reversible) Royal Flush for years while playing the Optimum Play machines on the very right of that bank at Red Rock. The bank I a refering to is located nearby the movie theater entrance. The highest level I ever saw was about 65,000 Dollars and from what I recall, the game people were playing was dd bonus. I took myself the time to check the pay-table and saw that it was a 8-5 game so even for short term players it could become very expensive. The winner was playing bonus poker, obviously trying to reduce the variance.
Could it be that this bank has a multi-game option with progressive individually in the sequential? I have never played this game for long and would only do it on a very special occasion, for instance, after hitting 2 Royals on the very same day and thus putting my luck the ultimate test and try a couple of hundred dollars or so.
Anyways, as long as the United States keep up with this C-19 travel ban for all international visitors, nobody from Europe who loves Las Vegas the way I do will be allowed to visit. Hopefully his spooky situation will pass by until summer 2021. Good luck, players.
I have hit several sequential royals in my career of 40 years. However none was on a bonus machine. Most were on holding ace or drawing one card
? Are the machines programmed to hit many less royals than reg machine
The ROI with perfect play is 104.02%, but the variance is 9869.44 versus just 21.28 for ordinary 6/5 BP. Still, many professional APs have a big enough bankroll to take a shot at this. The problem is that a nickel a hand is often not worth it to the APs who can afford the variance.
Off-topic, but last week in Biloxi, (Oct 2020) the Hard Rock has no Video Poker machines in their High Limit room. And worse yet, the few poker machines in the rest of the casino do not take your player’s card to be tracked. Is this the beginning of the end for Video Poker?
James,
Video poker offerings have been going downhill for many years. The pandemic has a tendency to strengthen trends already in place. (For example, online shopping, popular before the pandemic, is even more so today.) I am taking my mother to a local casino in Illinois this week. That casino used to have 25-cent full-pay 9/6 Jacks with a progressive. The best that casino has to day (according to VPfree2):
98.98% DDB: 25¢, 50¢, $1, $2, $5
98.89% SBDW: 25¢, 50¢, $1, $2, $5
98.85% SA: 25¢, 50¢, $1, $2, $5
I believe this deterioration is typical, and this trend is probably even more pronounced on the Strip than anywhere else in the country.
James August:
I have wondered for a while about exactly what you are talking about. The last time I was in Las Vegas, I could hardly find any video poker machines on the Venetian casino floor. It’s kind of a rule in Vegas that you always have video poker bar top machines, and I suppose that will never change, but they are usually Game King machines, so you can sit there and play Cave Man Keno if you want.
On the other hand, if you want to play Buffalo on the casino floor, go crazy. The damn things are everywhere and people love them.
Times change.
Mickey Crimm, the homeless change thief turned scavenger and AP wannabe claimed that 2-way SRF added 4.8%. Dumb MC can’t do AP-level math because he doesn’t get (a) convexity and (b) functions.
I wrote on VCT:
The fastest way to spot MC’s mistake is to use functions:
Y(1) = Beta1*(RF) + Beta2*(SF) + Beta3*(Quads) * Beta4*(FH) + Beta5*(FL) + Beta6*(ST) + Beta7*(Trips) + Beta8*(2 Pair) + Beta9*(Hi Pair)
Y(2) = BetaSRF*(SRF) * BetaRF*(RF) + Beta2*(SF) + Beta3*(Quads) * Beta4*(FH) + Beta5*(FL) + Beta6*(ST) + Beta7*(Trips) + Beta8*(2 Pair) + Beta9*(Hi Pair)
Y(1) is 96.8687% to 4 digits after the decimals point per WinPoker app. The Beta is the payout for that specific hand and the hand refers to the hand frequency. MC assumes the probability of each RF is identical, which is patently false (because probability of a $150K SRF > probability of a $1K RF).
Here is MC’s exact words on his 9/15/2020 tweet:
6/5 Bonus Poker is a 96.87% game. Royal odds are 40,236. Sequential odds are 120 X 40,236 = 4,828,320. Reversible Sequential is half that, 2,414,160. A $150,000 one-way sequential adds 2.4%, reversible adds 4.8%. So either 99.27% or 101.67%.
Effen’s answer is for perfect play so basic strategy will yield a lower EV or payback. I estimated 3% for 1-way SRF on VCT so 2-way would be 6% so I am off due to not adjusting enough for convexity, e.g. I screwed up in my Taylor-expansion series.
The fastest linear estimate of that $150K SRF would be to use Wizard of Odd’s article: https://wizardofodds.com/games/video-poker/tables/sequential-royal/
$150K SRF is 600,000 quarters; 600,000 / 5 is 120,000 for 1; so you substitute 120,000 for 1 instead of 10,000 for 1 (note 12X larger!!!) than in Wizard’s article. But Wizard’s article is for 1-way SRF so you would double it for 2-way SRF.
Caesar:
Those are the machines I miss!