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Figuring the Return for 8/5 Bonus Poker with Four Progressives

Note to reader: The original version of this contained an arithmetic mistake. It was pointed out to me by a man who posts under the name “New2vp”. The error, which affected one of the tables in the chart, are in the section relating to quad 5s-Ks. The corrected version follows. Thank you New2vp.

I received an email:  Sam’s Town in Las Vegas has three different banks of 8/5 Bonus. Two of those banks have progressives on the royal flush only. The third has that progressive, plus three additional ones for the quads: aces, 2s-4s, and 5s-Ks. Since the game starts out at 99.17%, sometimes these games must be pretty good. How do I figure out how to calculate the return of these games quickly if I don’t bring computer software into the casino?

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Promotion at Molly’s — Part II of II

In last week’s blog I described a loss rebate promotion at Molly’s, a chain of local 15-machine pubs in Las Vegas. I know many of my readers aren’t Vegas locals. While the specifics of today’s enhancement concern Molly’s, I’m hoping to make the discussion general enough so that it might be useful elsewhere as well.

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A Very Different Approach

On February 23, my blog addressed the subject of quitting while you’re ahead and other similar strategies that do absolutely nothing to the expected return of a game. I received a number of comments to that blog, including the one I’m going to share with you today: 

“I stop when I’ve won a decent jackpot, usually a four-of-a-kind that kicks out $200 or more. I’m good with winning a $200 hand. $200 will buy a nice evening out with my wife, so really, we both win.”

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Looking at 9-5 Double Double Bonus Poker with Multiple Progressives

The Vegas Stats & Information Network radio studio is located in the middle of the South Point casino floor, and periodically I’ve been a guest of the early morning show hosted by Paul “Paulie” Howard and Mitch Moss. Paulie mentioned that he found the DDB progressives interesting and wanted me to talk on the show about when you should get on the machine.

Such numbers do not make for good radio, especially since some of the listeners are probably driving to work and can’t take the time to write down anything. When I was last on the program on June 29, I gave some numbers and said that I’d be going into greater detail in my July 17 blog. And here we go!

If you’re serious about progressives, you should get Frank Kneeland’s “The Secret Guide to Video Poker Progressives.” That has by far more useful information on progressives than you’ll find anywhere else.

For today, I’ll assume you’re just going to be playing the game occasionally — and basically want to know how to figure the return on the game.

The game in question at the South Point contains a number of progressives, but does NOT have a progressive on the straight flush. Today I’m going to assign a number to the straight flush progressive because this same progressive is found in numerous casinos — sometimes with a progressive and sometimes without.

In addition to telling you how to evaluate the game, I also want to explain how I came up with the numbers. That way readers who are interested can apply the same technique to other progressives.

You’re going to need computer software to analyze progressives. I’m going to use Video Poker for Winners and WinPoker as those are the ones I use regularly and know well. If you have Wolf Video Poker, that can work as well. While it’s not quite as user-friendly, the wizardofodds.com has a free calculator you can use online. For many, it’s hard to beat free.

To start with, we need the base return of this dollar game, which is 97.87%. We’re going to be coming back to this base game over and over again.

To see how the progressive on the royal increases the return, I’ll set the royal on the game to 8000 coins. When I do this, I see the return is close to 100.13%. Assuming the return increases linearly (not completely accurate, but close enough for the analysis we’re going to be doing today), this means that when the royal increases $4,000, the value of the game increases 2.26%. Dividing by 4, when the royal increases by $1,000, the return on the game increases 0.56%. Once we have this multiplier, we can figure it out for any royal. Say the royal is at $7,356. That is 3.35 “$1,000 increments” more than the base game, and 3.35 * 0.55% adds 1.84% to the game.

Those who have actually followed along with the math will have noticed that I have rounded downward. The reason for this is that there are strategic changes to be made as each of the progressives change in value and it’s virtually impossible to get them all correct. By lowering the estimates of what the return will be, we somewhat take this into account.

Now we look at aces with a kicker. This jackpot starts at $2,000. So, we return to the base game and enter $3,000 for aces with a kicker. This gives up a return of 99.23%, which is an increase of 1.36% over 10 $100 increments, or 0.13% for every $100 (again rounding downward)

For aces without a kicker, this starts out at $800. Increasing that to $1,800 from the base game gives us 101.37% — an increase of 3.50% over ten $100 increments. So, whenever this progressive increases by $100, I add 0.35%.

For four 2s, 3s, and 4s with a kicker, this starts out at $800. Increasing that to $1,800 gives us 101.11% — an increase of 3.24% over ten $100 increments. So, whenever this progressive increases by $100, I add 0.32%.

I’m looking now at the straight flush, even though it does not have a progressive on the South Point machines. Sometimes, it does elsewhere. I’ll set the straight flush to $1,250 to get a return of 100.61% — an increase of 2.74% over ten $100 increments. So, whenever this progressive increase by $100, I add 0.27%.

The other two progressives, 2s-4s without a kicker along with 5s-Ks with or without a kicker, turn over fairly rapidly. These add some value, as you might collect $403 or $256 instead of $400 or $250 respectively, but these never get high enough to make that much of a “sit down and play or not” decision.

I assign 0.13% as the sum of these no matter how high they are. Why? Because that makes the base game an even 98% instead of 97.87%. This is a much easier number to work with, especially if I’m doing this in my head rather than with a calculator or some other means.

The final question you need to address is, “How high does it need to be before it’s worth playing?”

This depends on you. Since they have a number of 9/6 DDB games in the casino, which return 99.0%, the minimum sum of the progressives that you need is this figure. For players who wish to play a winning game, however, this isn’t nearly high enough.

You need 99.7% to make it an even game with the 0.3% slot club. Actually, that makes it slightly positive because you will also receive mailers and be able to participate in promotions while playing this game.

I can tell you I’ve seen it above the 99.7% level frequently. This is a decent game for dollar players to add to their repertoire at a casino with a number of good choices.

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A Different Way to Look at It

In Week 2 of my free video poker classes at the South Point, I usually teach beginning 9/6 Double Double Bonus Poker. Many of my readers wouldn’t be caught dead playing such a game. It returns only 98.98% when played well and there are plenty of better games around, at least in Las Vegas.

Still, players DO play this game regularly, so they might as well learn how to play it correctly. It might surprise you to know that in 2017, I played more coin-in on this game than any other! (It sure surprises me! If somebody would have bet me this five years ago, I would have bet against it. Of course, had I made a big enough bet, that would have affected the odds and I wouldn’t have played it more than any other!) While DDB is the most popular video poker game in the country, I didn’t play it because I particularly liked it. I played because with certain combinations of slot club benefits and promotions, this was the game that made the most sense to play.

In the class a few weeks ago, I was explaining that you NEVER hold a suited ace-ten in this game. One lady, who apparently goes for the royal every chance she gets, wanted to know how I could justify not going for the royal. The hand in question was A♠ T♠ 8♥ 7♣ 6♦.

As is my practice, I put this hand on Video Poker for Winners and displayed the results on the screen in front of the class. The display showed in Table 1:

 

[table “74” not found /]

 

After class I wondered if I could display these numbers in a way that would make more sense.I said holding the ace by itself was worth 21¢ more to the five-coin dollar player, and I pointed to the column that said holding the ace was worth $2.346 and holding the AT was worth $2.133. The lady nodded blankly, which told me she believed what I said, but these were just numbers. The numbers didn’t mean anything to her.
[table “73” not found /]

In this table, you have the value of each combination in dollars and cents (and tenths of cents.) That is, the chance you get a high pair (most frequently AA, but you can get JJ, QQ, or KK as well) is worth $1.274 when you hold the ace by itself but only $0.911 when you hold AT. This is a difference of $0.363. When you think about it, it’s not too surprising that you get fewer high pairs when you hold a ten in the hand. It both makes fewer “empty spaces” with which to make a high pair and when you pair up the ten, it’s not a high pair.

If you go through the differences on the bottom line, you’ll see that the two biggest advantages of holding AT (namely you can get a royal flush and you have a better chance of getting a flush) are worth almost a quarter apiece. But you lose in most of the other categories.

This chart is a little surprising to many players. After all, did you really think that the amount you get from high pairs is worth about half of the value of holding either the ace or AT? When you see these starting positions, you’re thinking four aces or maybe a royal flush. You’re not thinking of a measly high pair.

Don’t even think about trying to memorize these numbers. They are highly dependent on the exact five cards chosen. If one of the other cards is a spade, it greatly affects how much the flush draw is worth. If one of the other cards is a 2, 3, or 4, it affects both the chances for a straight, the chances for four aces with a kicker, and four 2s, 3s, and 4s with a kicker.

Is it useful to see how much each combination is worth in dollars and cents rather than in the number of occurrences? Maybe. Opinions will vary.

But if you think it’s useful, it’s already included in the Video Poker for Winners software. When you analyze a hand, you have a choice between “Show Possible Outcomes,” which gives you the information in Table 1, and “Show Coins Out,” which gives you the information in Table 2.

I didn’t know this was already included in the software until I looked while writing this article. I’m sure many of you didn’t know it either.