Ask the Slot Expert: Risk analysis and video poker, Part 2

Question: I usually play Hot Roll Video Poker, ten hands at 5-cent, 10-cent and 25-cent denomination. The game of choice is 8/5 Double Double Bonus or 9/5 for 25-cent denomination. This is all we have here in Boston. Each bet is $5, $10, and $25, respectively.

The question is: What is the bankroll requirement for each of these denominations to have a 1% and 5% risk of ruin?

Answer: This week we'll take a closer look at one of the products that analyzes your risk playing video poker, Dunbar's Risk Analyzer for Video Poker, a set of Excel macros.

You can read about the math behind how the Excel macros work in Risk of Ruin for Video Poker and Other Skewed-Up Games. Following the article can be rough sledding at times, but it's very similar to many of Don Catlin's articles on this site. Both authors start with a simple formula, build on it to progressively more complex formulas, and arrive at a solution for the problem at hand. You may have to read the article a few times -- I did -- paying attention to how Dunbar uses things we learned before in each step.

At least there's a minimum of Greek letters. I don't remember being overwhelmed by Greek letters in my first semester of statistics. But the second.... Every formula looked like a Greek Scrabble tile rack. The first semester professor was from Bath, Maine. He had a vaguely British-like accent. The professor for the second semester had a heavy Eastern-European accent. And bad handwriting. We should have had a lesson on the Greek alphabet before starting with the math.

For a description of the many capabilities of the macros, see Henry Tamburin's interview with Dunbar.

As I said before, the Risk Analyzer is a set of Excel macros. The product ships as an XLS file that you open in Excel.

I'm using it for the first time. Let's see if I can answer this question: How large a bankroll do I need to have a 5% risk of ruin playing 10-hand 9/5 Jacks at $25 per play. For the time being, we'll ignore the Hot Roll gimmick. As I said last week, the Wizard of Odds was kind enough to show us that the math of the Hot Roll gimmick makes the long-term payback for a Hot Roll paytable the same as the paytable without the gimmick. The only thing we buy with the extra bet that activates the gimmick is increased volatility.

The first step after opening the workbook file in Excel is probably to enable the macros, now that Microsoft is taking security seriously. (Many years ago at Windows programming seminar, the speaker was teaching how to use a particular API call in Windows. One of the parameters was a security object. He said, "Of course, we pass in NULL. Probably shouldn't, but that's what we do.")

Next, choose menu item 2, START CALCS, from the Main Menu.

Now we have a choice. We can either analyze one game or a series of games. The latter option lets you calculate bankroll requirements for a buffet of games you plan to play on a trip. We only want to analyze 9/5 Jacks, so we'll pick that in the Select One Game dropdown and click the GO button.

Next you get a rather intimidating page of boxes of different colors. It's much like a crap table -- you can ignore most of it until you want to use a feature. There's a good help screen you can bring up. Plus, the screen has text to guide you through the steps. You enter parameters in the yellow boxes. The blue boxes have captions and calculation results.

Step 1 is entering the parameters for the calculations. We want to play 10 hands, quarters, 10 coins per hand. Enter 0.25 for Coin Size and 10 for Number of coins. And this is a good time to notice that to the left of where we're entering this data is a dropdown to let us specify the number of lines we want to play. Choose 10-play.

Let's leave the rest of input boxes blank, even Hourly cost of errors. We all play mathematically perfectly, don't we?

Step 2 tells us to click on a button to calculate either the Long-term or Short-term RoR (Risk of Ruin). We didn't enter anything into the Trip RoR parameters box above the Short-term button, so let's click Long-term. A warning pops up: "The game you have defined has no longterm player advantage. Therefore, the longterm risk of ruin will be 100% regardless of the size of the bankroll." The warning box goes on to ask if we forgot to include Cashback (which may make the game positive). Finally, "it IS possible to do Short-term risk of ruin calculations even when a game has no long-term player advantage."

We're still in business. We'll have to go back to the Trip RoR parameters we ignored before so we can run short-term calculations.

We have to switch from the long term to the short term. Time on video poker machines is measured in number of hands not ticks of a clock. The page wants us to enter how long we want to play and how quickly we play.

I almost always play a certain number of hands and I don't know how quickly I play and I don't keep track of how long I play. I think most VP pros also plan to play a certain number of hands, especially when a point multiplier is capped. (I learned the hard way that casinos notice if you always quit playing once you've maxed out. Don't do that.) The product is the only thing that matters. We can just enter any two numbers that yield the number of hands we're going to play when multiplied.

It's usually very easy for machine players to know exactly how many hands or spins they've played by looking at the slot club display. Table games players usually aren't tracked as finely. They don't know how many hands they've played. The table games players I know usually plan to play a certain length of time.

We have to enter the number of hours we want to play and the number of hands we play per hour. My correspondent didn't give this information, so let's guess. He's in Boston so I'll guess he's local and we'll plan on a day trip of four hours playing 400 hands per hour. We also have to enter our bankroll.

Wait a minute! Isn't that what we're trying to calculate?

Yes, it is. But there's a problem. The analyzer can take a bankroll, a paytable, and the number of hands played and calculate risk of ruin. But it's a one-way street. We can't start with the desired risk of ruin and other parameters and work our way backwards to bankroll. We can find the bankroll that will give us the desired risk of ruin, but we'll have to try multiple bankrolls to home in on the desired result.

Let's bring $1000 to the casino. Probably not nearly enough to play $25 per hand, but our risk is spread over 10 hands. Click Calc Short-term RoR and the answer appears quickly. That bankroll gives us a 69% RoR.

Yikes. Let's try $2000 just to see how quickly the RoR falls. RoR is now 29%. Sweet. We may not need a wallet overflowing with Benjamins to reach our goal.

I tried various bankrolls and got about a 5% RoR at $3075. About $3700 will give an RoR around 1%.

Two things to keep in mind. We're not dealing with the increased volatility for Hot Roll, so the bankrolls will really need to be a bit higher.

The other thing to keep in mind is randomness. One of the short-term parameters is Number of trials. The process plays the number of hands you specify that many times and keeps track of the results of each trial. The default number of trials is 1000. You won't necessarily get the same RoR each time you calculate with the same parameters.

Sometimes you're lucky. Sometimes you're not. Sometimes the process is lucky. Sometimes it's not.

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