An interesting article was recently published by FrankB on the gamblingwithanedge.com blog. (I think of that page as “my page” because GWAE is “my show.” In fact, I’m only a co-host on the show and one of many gambling experts who publish on that page — which is hosted by Anthony Curtis’ Las Vegas Advisor. Whether it’s my page or not, I’m proud to be associated with it.)
FrankB is a friend, and quite expert at figuring out combinational mathematics, among other things. Doing it the way he did, his 1-in-288 million is computationally correct. But I have a major bone to pick with doing it that way.
The problem is that this was done “after the fact,” and then the math assumed you took the exact same path as happened in real life. What’s wrong with that? Well, you can do this and make the number however large you want.
If you decide that being in diamonds is an important part of the story, then multiply your 1-in-288 million by 1/4 and come up with more than 1 in a billion. If you think that specifically starting with KQJT suited is important, multiply a factor of 1/5. If you think that having the cards in the exact order of K Q J x T is important, multiply the number by 1/60. Using all the multipliers, you can get 1 in 350 billion, which is 1,200 times as large as the paltry 288 million. Now we’re talking!
Why would anybody do it that way? People like to tell stories that are very, very unusual. Which proves they were very, very lucky. (Or unlucky — depending on how you like to tell stories.)
In fact, we’re talking about taking down the royal-on-all-three-hands, and that is “merely” 1-in-650,000. (Actually, 1 in 649,740.) If you’re planning on taking down the progressive, THAT’s the number you’re thinking about. Sometimes the “backdoor” method of being dealt 4-to-the-royal and hitting three times wouldn’t pay off. Some of these machines specifically say, “Dealt Royals Only,” which guards the casino against this 1-in-288 million longshot. And, if you ask me, it’s pretty chintzy on the part of the casinos that do this.
If you want to add the 1-in-288 million to 1-in 649,740, (assuming you’re at a place where both ways will pay you off), you get all the way up to a robust 1-in-648,285 — which is still going to be rounded off to 1-in-650,000 for most people explaining it.
So, is this a 1-in-288 million jackpot or a 1-in-648,285 jackpot? Take your pick! When you figure this out after the fact, either number can be justified. As can several other numbers as well. It’s the same $12,280.25 jackpot, which most of us would call a very nice hit.
An interesting question, to me anyway, is how much does this “dealt royal” bonus add to the EV? To figure this, I use $3,000 as a normal amount for three $1,000 royals. Once you know this figure, it’s easy to adjust to the actual number.
It’s quite simple. Every 650,000 hands (using rounded numbers), you get another 800 coins per coin bet. And 800 / 650,000 = 0.0012 = 0.12%.
On this game in particular, where the individual progressive royals averaged a bit more than $1,800, the game itself was worth 99.6%. Add in two extra 0.12% bonuses, and then some, because the dealt royal bonus is based on $12,280 in this case and the undealt royals added up to $5450 or so. Call that 99.9%, with 0.3% of that based on the 1-in-650,000 dealt royal.
The signage on the machine implies it’s a Boyd property machine and they regularly have 11x points for senior days and sometimes at other times. Eleven times multiplier (their base rate is 0.05%), adds another 0.55%. That makes the game worth 100.45% before including the meter progression and the extra benefits. (There is usually a senior drawing of some sort available, possibly a free buffet, plus some people get mailers. If you play enough, hosts also sometimes give you meal comps, etc.)
This was definitely a mildly positive play — the player got lucky and got a good story. The picture was taken, and this is at least the second major article written about the hand — plus I know it was spoken about on at least one radio station.
And I still think 1-in-650,000 is a much more valid number than 1-in-288 million. I don’t think it is worth an extended argument — but obviously I did think it was worth an article.
Author’s note: I passed this article by FrankB and Anthony Curtis before publishing. I’m friendly with both and want to keep it that way. Frank responded (I’m shortening his response but not changing his intent, I believe).
“I don’t necessarily have a problem with it. The uniqueness of how they got to that end result was what I thought people would find interesting and have. . . . Regardless of how others chose to view it, I think it’s the most interesting hand I’ve ever seen.”
While there is a lot of overstating the rarity of events for exactly the reasons you point out, Bob, I think Frank’s use of the 288 million figure is entirely reasonable in this case. If you were analyzing this play ahead of time, you’d want to know the chance of getting 3 RF’s. One way to get 3 RF’s is to be dealt 4-to-an-RF and then connect on all 3 hands. As you point out, the effect on the overall odds from this route is negligible. It’s negligible precisely because it’s a 1 in 288 million shot.
Your point about people putting after-the-fact specifications into the calculation is right on the mark. But in this case, I don’t see any extraneous specification that can be pointed to, once you accept the assumption that the goal was 3 RF’s.
I would not recommend to play 3x Play Progressive in order to score big on such a long shot. Although I actually did have 3 royals dealt to me over the course of 10 years’ time ( and I am a regular Tourist visiting Vegas just a couple of times per year), it seems to me a bit hard to go for it.
In addition to that….I haven’t found a good paytable on Triple Play progressives yet. Sounds funny, but once in a while, the Tuscany has extremely large progressive jackpots on the nickel game 10 Play. I’ve sometimes seen it at 15,000 Dollars and higher , although the basic game has a terrible paytable. If anybody can share the secret about where to find the machines with great paytables on 3x Play progressives, such infos are Always appreciated.
Greetings
Of course I can appreciate the fact that it’s an after-the-fact observation. I see a lot of pics of VP hands and rarely do I look at one and react with a ‘never seen that one before”. The objective was to share something that I’ve never seen or even considered and I’m guessing few will ever see again while putting it in some kind of fun perspective.
We all know that anytime you play a hand, the five cards you’re dealt are as unique and rare as any other hand – whether it’s a dealt spade RF or 5D 4H JD 10C 8S. They’re the same in that regard. Some combinations just mean more and this hand was interesting enough due to the circumstances and the way they achieved it that I wanted to share my fascination with it.
And example of why the one in 288 million figure is specious is the odds of my eating the particular egg I had for breakfast this morning. It came from a carton of a dozen eggs so the odds were one and 12 that I would’ve eaten that particular egg this morning. that’s because the situation was already set where that egg was in the carton of 12 eggs. This is the pre-existing starting point for this situation, like being dealt four to a royal flush on the three play machine. To go back and trace this egg back to the egg farm (or whatever they call those places that eggs come from), and point to it and say what are the odds that I would be eating that particular egg this morning we would have to say that the odds would be astronomically small. To extend the Video Poker analogy back further you could make her odds even more astronomically small by asking not only what are the chances that she got this particular hand, but why not add what are the chances she got this hand on this particular machine on this particular day. Then you would really see some astronomically small odds!
Hi Frank,
I am guessing your mathematical exhibition will be read as “I’ll -never- see a dealt royal flush,” even though your analysis addresses a completely different (and decidedly more interesting) problem. One in 300 million is rarer than rare–almost unique, but one in several hundred thousand is “due” for the enthusiast who has a couple million hands under h/er belt.
I think Bob–as one of the high priests of the Expected Value gospel–is not being as direct as he could in his liturgy here: Bob seems to be burying the rare event of making all three royals on the draw under the more common event of being dealt the royal and calling each the same. In terms of relative likelihood, one is a midget and the other a mammoth, but the article reads as if they are on equal footing for worries of losing a few parishioners.
Trying to make sure I follow the math on the 0.12%. If I was playing a base Double Double at 98.98% and the dealt was at $21k would that be worth 0.84% (7*.12%) + 98.98 = 99.82 plus cash back rate, un-dealt royals, etc? Just want to make sure I understand the concepts. Thanks!
“Trying to make sure I follow the math on the 0.12%. If I was playing a base Double Double at 98.98% and the dealt was at $21k would that be worth 0.84% (7*.12%) + 98.98 = 99.82 plus cash back rate, un-dealt royals, etc? Just want to make sure I understand the concepts. Thanks!”
No, that’s not it. You’re not including the values of the existing royals and you’re counting some of them twice.
Assume, to make the math easier, that the three royals were at $1,000, $1,200, and $1,4,00 — in addition to the dealt royal being at $21K.
since the average of the three royals is $1,200, 9/6 DDB with a $1,200 royal is worth 99.54%. These three royals add up to $3,600 and that would be part of the $21K. The $21K would be an EXTRA $17.4K, which will add another 0.52% (saying an extra $3,000 is worth 0.12% is the same as saying an extra $1,000 is worth 0.04%. Multiply 0.04% by 17.4 and you get about 0.52%.)
Hope that helps.
Thanks Bob! I appreciate you coming back and helping! Been a fan since the days of the Skip Hughes VPHomepage…. 🙂
I plugged the $1800 royal into WinPoker and came up with a return of 100.505%. Am I doing something wrong?
I am from South Africa and very new to video poker and very anxious to learn. I visited our brand new casino at Menlyn Maine. I noticed the payout for double double bonus on R1. 00 coin machine with a full play of 10 coins, R10 is 12/10. The full house pays 12 and the flush 10. I seek advice how to play this machine. I can’t find any tips for this payout.
“And example of why the one in 288 million figure is specious is the odds of my eating the particular egg I had for breakfast this morning. ”
Jerry, just to show that your example is specious…exactly how much bonus did you get for eating that particular egg that morning? Is it worth my calculating the odds of getting an egg like yours? Where can I find a restaurant, casino, or home offering me the special egg bonus?
Yes, it’s easy to point to rare events. That doesn’t make the calculation of odds of certain rare events less meaningful.