Ask the Slot Expert: Risk analysis and video poker, Part 1

Question: I was wondering how much you would charge to assist me in determining the size of the required bankroll for a video poker variant I play.

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?

Also, is it possible to make any money at these games or are they practically unbeatable?

Answer: It's your lucky day. Your only charge for this advice is reading my columns.

Speaking of lucky days, when I worked for Pan Am I sometimes had to work at JFK to fill in when the gate agents were on strike. At the start of my first deployment, Pan Am management knew it was going to be rough, so most flights were cancelled. The evening goal at JFK was to get just three of the evening flights out. It was probably two London flights and one to Frankfurt.

The supervisors told us to just get people checked in and print their boarding passes. We were not going to deal with excess baggage charges.

I think management had in mind that we would be looking the other way when passengers had an extra bag or two. I don't management had in mind the family I dealt with.

They had so many trunks even Queen Victoria would have said, "Guys, you overpacked."

I don't know how much excess baggage charges were back in the mid-80s when you were allowed to check a bag or two without being charged. I bet Pan Am's largess on that night saved them hundreds of dollars, if not even a thousand or more.

I always thought the Risk of Ruin calculations required a positive expectation game. If you're playing at a disadvantage, your risk is 100% -- you will eventually lose all of your money. The Wizard of Odds page Video Poker: Bankroll Size vs. Risk of Ruin seems to confirm this. The three tables on the page are for paytables that are either positive on their own or positive with cash back.

The Wizard's site also has a Risk of Ruin Calculator. One of the inputs to the calculator is the player's advantage. The instructions for that parameter do not mention entering a negative number for player disadvantage.

At the bottom of the page is a link to Risk of Ruin for Video Poker and Other Skewed-Up Games. In this context, skewed-up just means that some of the payoffs on a bet are very large compared to the bet, e.g., 800 units for a royal flush.

The article describes how to derive a risk equation using the risk of ruin for a 1-unit bet [R(1)] "for any game with a constant set of payouts that occur with a prescribed frequency." It continues, "If a game does not have a positive expectation, then the smallest positive solution for R(1) is 1 [100%], reflecting the fact that ruin is inevitable."

Hot Roll Poker is a multi-line game with a gimmick. If you double your bet, you will occasionally be rewarded with a multiplier. The value of the multiplier is determined by rolling a pair of dice.

Does the gimmick turn any Hot Roll Poker paytable positive? I don't think I've ever seen a gimmick machine that's positive. Most of those machines have middling or worse paytables, giving one the impression that the gimmick makes up for the lousy paytable. Let's take a closer look at Hot Roll Poker.

The Wizard has come through for us again on Hot Roll Poker, last updated on May 1, 2019. There's an amazing symmetry in the math of this game.

According to his page, the player has a 1 in 6 probability of getting a multiplier. The average result when rolling two dice is 7. Thus the average multiplier the player gets is (1/6)x7 + (5/6)x1 = 12/6 = 2. Because you have to double your bet to qualify for the multiplier, the return when enabling the Hot Roll is the same as that of the paytable. The only thing you're buying with the additional bet is increased volatility.

According to the Wizard, the long-term payback of 8/5 Double Double Bonus is 96.79% (Yikes!). Stick with 9/5 Jacks at 98.45% unless you don't mind feeding the machine in between rare rushes of joy after hitting premium hands.

Despite the fact that all the Hot Roll paytables you play are negative expectation and no casino offers enough cash back to turn them positive, all is not lost. One of the authors of the skewed-up article is Dunbar. He developed a Risk Analyzer program for video poker. Henry Tamburin published an exclusive interview with him. (Take that, Oprah. You can have Harry and Meghan. Henry got Dunbar!)

The "interview" about Dunbar's Risk Analyzer for Video Poker reminds me of the Honeymooner's sketch about the Handy Housewife Helper.

"Can it do this?"

"Yes, it can."

"Can it do that?"

"Yes, it can."

Like the Handy Housewife Helper, Dunbar's Risk Analyzer can also "core a apple."

Can it calculate the probability you will go broke playing a given game for a given length of time with a given bankroll? Yes, it can. (For example, quarter 9/6 Jacks, 400 hands/hour for 4 hours, $200 -> 8% chance of going broke.)

Can it handle multi-line games? Yes, it can. (You have a 55% chance of going broke playing that same $200 bankroll on a quarter 9/6 Jacks Triple Play machine.)

Can it tell you the chances you will ever be ahead by a certain amount? Yes, it can. (E.g., dollar 9/6 Jacks, 20 hours at 400 hands/hour, 22% chance you will be ahead $1000 at some point.) (Can someone tell me why this is useful? It seems like trivia to me. How would one use this factoid? How would it change one's behavior?)

Next week, we'll continue looking at risk and bankroll in video poker. But let's address your last questions before we go.

It is possible to make money playing a negative expectation game. There may be times when you are ahead overall, especially when adding in cash back and the value of comps. But the lower the overall payback and the longer you play, the more difficult it will tend to be to be ahead.

I say "tend to be" because Frank Scoblete has written about a couple that claims to be a long-term winner playing Joker Wild in Atlantic City. That's a decidedly negative expectation game, yet they claim to be ahead.

I guess there are always a few outliers.

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