Four to a royal loser promo

About 50,000 years ago, there was a short-lived promo at the Tuscany. If you finished with a losing hand that was also four to a royal, you would get a 100-coin bonus. In other words, AKQJh3c was a bonus hand, but AKQJhJc was not.

The local bottom-feeders showed up precisely at 10 am--when the promo started--and burned it out within two hours. They rushed to the dollar machines, sat there until 10:00:00, and started playing like madmen. Every machine was taken. Soon, the air was filled with calls for the (grand total of three) changepersons to come and pay me my goddamn 100-coin bonus. Those poor people were scurrying around, and none of the flea-P's ever tipped anyone. To add insult to injury, three $1 royals were hit in the first hour--also with no tips to the changepersons.

I had gotten there an hour early and was playing .50 10/7 DB. Ironically, I hit a royal before the promo even started (and I tipped $50). When the promo started, I got a couple of bonus hands, but it was taking 15-20 minutes to get paid. At noon, Tuscany management abruptly canceled the promo.

Now, I have a couple of interesting, if purely academic questions. First, I decided that dealt four to a royal and an odd fifth card (i.e., no pair, straight, or flush), one should HOLD ALL FIVE cards, hit the draw button, and collect the bonus. I'm fairly sure this was a dumb idea, though, since if you drew as normal, you would have a shot at the royal and half the time, you would get your losing bonus hand back anyway. Was I correct or not (it never came up, ironically)? What is the EV of a hand like AQKJx with the 100-coin losing hand bonus (assuming you do draw a card)?

Also, can you guesstimate how much this added to the game's EV? It sure drew in the fleas, so I guess it was plenty worthwhile. But I have no idea how much.

Could be a good promotion for pulltabs at bartops where there is always someone nearby to pay out and the added value is only like $5 instead of $100

Quote: Joeshlabotnik

First, I decided that dealt four to a royal and an odd fifth card (i.e., no pair, straight, or flush), one should HOLD ALL FIVE cards, hit the draw button, and collect the bonus.

You're losing $85 in value in just the 1-in-47 shot at a royal, plus losing 15-20 minutes of being able to play a truly great game. Go for the $4,000

Obviously the optimal play is to go for the Royal.

If you currently have a losing hand, out of the 47 remaining cards you obviously have the one jackpot card. You have 12 cards that will give you five credits. 3 straight cards and 8 flush cards. That leaves 23 other losing cards so not counting the Royal it's exactly 50-50

Quote: Joeshlabotnik

Now, I have a couple of interesting, if purely academic questions. First, I decided that dealt four to a royal and an odd fifth card (i.e., no pair, straight, or flush), one should HOLD ALL FIVE cards, hit the draw button, and collect the bonus. I'm fairly sure this was a dumb idea, though, since if you drew as normal, you would have a shot at the royal and half the time, you would get your losing bonus hand back anyway. Was I correct or not (it never came up, ironically)? What is the EV of a hand like AQKJx with the 100-coin losing hand bonus (assuming you do draw a card)?

Also, can you guesstimate how much this added to the game's EV? It sure drew in the fleas, so I guess it was plenty worthwhile. But I have no idea how much.

Question 1

With respect to the first question, I would suggest that you have chosen the Royal Draw with the lowest value coming from the Royal Draw, (KQJ10 gives a straight flush opportunity, as well) but we'll go with that and you'll see that throwing away the losing card is the better play even with the promotion.

First of all, you are 1/47 to get the Royal, so that's 85.11 coins (rounded).

You are 8/47 to get some other Flush, so that's 5.96 coins.

You are 3/47 to catch an off-ten straight, so that's 1.6 coins.

You are 12/47 to catch a high pair, so that's 1.28 coins.

Finally, you are 23/47 to have a different losing hand, so that's 48.94 coins.

The expected value of tossing the losing card is approximately 142.89 coins.

Thus, the decision is not even close.

Question 2

You would really have to look at games individually, and also the strategy would likely change significantly in order to garner optimal EV from the promotion, so something like that is way above my pay grade and more for someone like the Wizard!

Just for one example, Js-Jd-Qh-Kh-Ah is actually a very close decision in that game with holding the jacks being the better choice:

1.456244 Bets (Jacks)
1.424607 Bets (Three-to-a-Royal)

However, a promotion such as this would make holding three-to-a-royal a no-brainer because you are going to get nearly a full unit (educated guess-mental math) just from the probability of getting paid twenty bets to hit a Royal Card (2/47) and miss a paying hand. In fact, let's take a look:

If you hit the ten of hearts, then the following cards result in a losing hand:

2's (3)
3's (3)
4's (3)
5's (3)
6's (3)
7's (3)
8's (3)
9's (3)
10's (3)

Thus, you have 27 cards that would still result in a losing hand, rendering the expected value ONLY on catching a ten and missing a paying hand as such:

((1/47 * 27/46) + (27/47 * 1/46)) * 20 = 0.49953746531

Now, if you hit the Jack, then all of the same cards result in a loss, except the ten, because any ten gives you a Royal or a Straight, so there are 24 losing cards:

((1/47 * 24/46) + (24/47 * 1/46)) * 20 = 0.44403330249

The result of that is catching a Royal card and then missing adds about 0.9435707678 in value making the overall value (which, of course, includes winning hands) 2.3681777678 which far surpasses holding the Jacks.

The value increase on a hand such as three-to-a-royal will remain reasonably constant at between .9 units and 1 unit, I would suggest, so any Three-to-a-Royal is going to beat any high pair, or two pair with three Royal cards in it such as Kh-Kd-Qh-Qd-Ah.

While one could say that Three-to-a-Royal is a close decision on that game compared to keeping a high pair (in fact, sometimes you do keep Three-to-a-Royal anyway, if there is a straight flush chance and more straight opportunities) but under normal conditions, two pair is always the correct hold. In the case of this Promo, however, you would toss the two pair.

___

There may also be some two-to-a-royal holds that get interesting such as:

As-Ks-Qh-Jh-3c

Keeping the four high cards is generally better by about .101203 units, however, if we look at the probability of catching two of the Royal cards holding Qh-Jh:

nCr(3,2)*nCr(44,1)/nCr(47,3) = 0.0081406105457909

Okay, so we take this: 0.0081406105457909

We will call it 25 losing cards with that just to keep it simple:

((0.0081406105457909) * (25/45)) * 20 = 0.09045122828

So, that adds roughly .09 units, and we may or may not keep the four high cards, I would have to look at every possible combination of the two cards to know exactly, but even if we assume we are left with 27 losing cards, it still doesn't quite bring it up to that .101203 threshold.

However, in some instances (namely suited J-Q) it would make the Two-to-a-Royal better than three consecutive to a straight flush with no high cards.

Quote: Joeshlabotnik

About 50,000 years ago, there was a short-lived promo at the Tuscany. If you finished with a losing hand that was also four to a royal, you would get a 100-coin bonus. In other words, AKQJh3c was a bonus hand, but AKQJhJc was not.

The local bottom-feeders showed up precisely at 10 am--when the promo started--and burned it out within two hours. They rushed to the dollar machines, sat there until 10:00:00, and started playing like madmen. Every machine was taken. Soon, the air was filled with calls for the (grand total of three) changepersons to come and pay me my goddamn 100-coin bonus. Those poor people were scurrying around, and none of the flea-P's ever tipped anyone. To add insult to injury, three $1 royals were hit in the first hour--also with no tips to the changepersons.

I had gotten there an hour early and was playing .50 10/7 DB. Ironically, I hit a royal before the promo even started (and I tipped $50). When the promo started, I got a couple of bonus hands, but it was taking 15-20 minutes to get paid. At noon, Tuscany management abruptly canceled the promo.

Now, I have a couple of interesting, if purely academic questions. First, I decided that dealt four to a royal and an odd fifth card (i.e., no pair, straight, or flush), one should HOLD ALL FIVE cards, hit the draw button, and collect the bonus. I'm fairly sure this was a dumb idea, though, since if you drew as normal, you would have a shot at the royal and half the time, you would get your losing bonus hand back anyway. Was I correct or not (it never came up, ironically)? What is the EV of a hand like AQKJx with the 100-coin losing hand bonus (assuming you do draw a card)?

Also, can you guesstimate how much this added to the game's EV? It sure drew in the fleas, so I guess it was plenty worthwhile. But I have no idea how much.

Obviously what spiked your comment on this was my comment in another thread where I used that as an example of where a class II could mess with your strategy because if you got any pay (even Jacks or better) they wouldn't pay you. I do take offence at you calling people bottom feeders who played this because I played it along with many other well known pros/ AP's. We locked up the best machines at least 4 hours in advance, and It was very lucrative.

Im not even sure how anyone got any good machines if they showed up just before the promo started as we had problems getting everyone down at least 4 hour's prior.

I don't think the "bottom feeders" couldn't afford this play, especially on higher denominations. They actually ran it 2 times as did multiple other casinos during that time IIRC the silver nugget ran it the week before. At one time It was worth over $100 an hour. They even had multi line dollar's.(If bottom feeders are making over $100 and hour, count me in, especially if you have 4 or 5 people playing for you) I don't know why you think it only lasted for 2 hours. For us it lasted entire length of the promotion. At some point they may have started slow paying.

I and people I work with always tip well, especially during promotions. We actually tip much better than the average person. I have given $100 multiple times on a 1k Royal and even split entire drawings with employees.

Quote: AxelWolf

Obviously what spiked your comment on this was my comment in another thread where I used that as an example of where a class II could mess with your strategy because if you got any pay (even Jacks or better) they wouldn't pay you. I do take offence at you calling people bottom feeders who played this because I played it along with many other well known pros/ AP's. We locked up the best machines at least 4 hours in advance, and It was very lucrative.

Im not even sure how anyone got any good machines if they showed up just before the promo started as we had problems getting everyone down at least 4 hour's prior.

I have no idea what comment of yours you're referring to, so no, that comment didn't induce my posting this thread.

Well, then, we must have been there at different times. They must have run the promo more than once. I remember I was kicking myself for not getting there any earlier than 9:00. The place was nearly deserted then. I played the .50 DB because I didn't have the cash on hand to sustain the play at dollars, and I thought that I didn't have time to stop at the ATM (and I would have only gotten another $300 anyway, damn banks). I had only heard about the promo when I read an email at 8:00 that morning.

It was like somebody rang a gong. At about five minutes before 10:00, people started streaming in. Everybody sat down at a machine and just waited for the clock to strike ten. Anyway, just after noon, a casino manager announced to all and sundry that they would no longer be paying the promo. So no, you must not have been there then.

I was furious when I learned later that the main reason for the promo being killed was that beleaguered slot change persons were complaining to management about how the bottom-feeders were treating them, being imperious with their demands to hurry up with the bonus payments so they could resume play. And yes, when I gave one of them $5 when she paid me my $50 bonus (.50 game), she said, "You're the first one who's toked me the whole morning." This was about 11:30, so she had probably paid out dozens of bonuses. Another change person told me he had paid out all three $1 royals, and had been stiffed three times. (I knew a couple of the change persons, and I can vouch for the fact that all of them were royally pissed off and complained to management. I also saw one guy--who had already hit a royal--yelling at one change person to GET OVER HERE AND PAY ME MY BONUS.)

So you probably weren't there that day. I'm not even sure that they killed the promo for good then, or just for that day. But I saw it as a prime example of greedy fleas burning out a terrific play. All they had to do was not act like jerkwads to the poor change people, and maybe loosen the purse strings a little and toke something. But if there's one constant about APs in Vegas, it's that they always get greedy and burn out whatever good plays exist--and the diminishing of good plays just makes that effect even worse.

Quote: Mission146

However, in some instances (namely suited J-Q) it would make the Two-to-a-Royal better than three consecutive to a straight flush with no high cards.

Thanks for your answers to my questions re the strategy. I was fairly sure I was wrong to hold the 4RF+x, but fortunately, the hand never came up. I was thinking at the time that there would be a lot of other strategy variations on any JOB/DB game, but I didn't have the tools, or the time, to figure them out.

I still do wonder how much this was worth in +EV terms. I used the very rough estimate of hitting one bonus an hour at my normal speed of 800 hph. Thus, I would get twenty extra bets every 800 hands, or a tidy 2.5%. Of course, it may have been much better than that.

1. Don't be rude to employees.
2. Tip the slot attendants (IMO at least 1%).
3. Don't be an a**hole to other players.
4. If it's a good promo or a strong play, be extra nice to employees and tip extra.


People significantly over-estimate how much tipping costs them. For instance, on a game where only RF is a taxable, tipping 10% of the handpay cuts your return by 0.2%! Not saying you should tip that much, but it goes to show how much you can tip and how little it hurts you. (Unless you're trying to squeeze out that extra 0.01% return because that's "way too much", in which case, IMO, whatever you're playing isn't worth playing.)

Quote: Joeshlabotnik

Thanks for your answers to my questions re the strategy. I was fairly sure I was wrong to hold the 4RF+x, but fortunately, the hand never came up. I was thinking at the time that there would be a lot of other strategy variations on any JOB/DB game, but I didn't have the tools, or the time, to figure them out.

I still do wonder how much this was worth in +EV terms. I used the very rough estimate of hitting one bonus an hour at my normal speed of 800 hph. Thus, I would get twenty extra bets every 800 hands, or a tidy 2.5%. Of course, it may have been much better than that.

You're welcome, I could definitely understand not having the time or the tools to figure them out. Honestly, Three-to-a-Royal over a high pair or two pair is worth a ton, and three-to-a-royal would also be better than any four-to-a-flush, with exception to four to a straight flush, which would still be better. Those are definitely the biggest EV changers and probably the three most common.

I dug around a little and your estimate seems pretty good; From:

https://wizardofodds.com/ask-the-wizard/video-poker/probability/

Quote:

In 9/6 Jacks or Better with perfect strategy you will see a royal on the draw once every 40,601 hands, but four to a royal once every 460 hands. For every royal you see, you will be one card away 88.33 times. Of the four to a royal hands, 50.37% will pay nothing, 24.89% will pay as a pair, 7.89% as a straight, 16.16% as a flush, and 0.69% as a straight flush. Here are the exact numbers.

Thus, you have four to a royal once every 460 hands of which 50.37% are losers, so about once every 913.24 hands. Given the differences in plays that we would be doing (as mentioned above) I could see that getting down under 1 in 900 hands, but probably not quite down to 1 in 800.