Ask the Slot Expert: Risk analysis and video poker, Part 3

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: Last week I used Dunbar's Risk Analyzer for Video Poker, a set of Excel macros, to try to answer this question. I simplified the analysis by ignoring the Hot Roll aspect of the game and just analyzing 9/5 Jacks. This week let's bite the bullet and see if we can analyze the game with the Hot Roll gimmick.

If you want the backstory, see my last two columns. You can read about the math behind how the Excel macros work in Risk of Ruin for Video Poker and Other Skewed-Up Games. For a description of the many capabilities of the macros, see Henry Tamburin's interview with Dunbar.

The Analyzer lets you enter your own custom paytables. The Wizard of Odds was kind enough to share the math of the gimmick on Hot Roll Poker. The Wizard tells us that the probability of getting a multiplier is 1/6. So 5/6 of the time we'll get the base payout for a winning hand and 1/6 of the time our winnings will be multiplied by a multiplier. The multiplier is determined by rolling two dice. We could add paytable entries for each total of two dice -- actually we can't because we can't enter that many paytable lines -- but we don't have to. We can just use the average sum of two dice, which is 7.

For our custom paytable, we have to make two entries for each paying hand, one base and one multiplied. We take the payouts and probabilities from the non-gimmicked paytable and multiply the probabilities by 5/6. For the multiplied entries, we multiply the probabilities by 1/6 and payouts by 7.

Let's create our new paytable. We can use a shortcut to do some of the work for us. From the Game Selection screen, choose 9/5 Jacks and click the Go button. Next click the To MAIN MENU button. Click START CALCS and then CUSTOM GAMES. Click No to say we want to create a new custom game. Click Get the Last Active Game button to fill the paytable with 9/5 Jacks.

Now we have to alter the probabilities displayed and add new entries for a multiplied win. When we're done entering the data, click Use Table Info and then Yes to save the paytable. Enter a name for the paytable and click OK.

Now we're on the calculation page. The data in the blue paytable box looks good, except for one thing. The return calculated for the paytable is 196.94%. Something's not right. The Wizard told us that the long-term payback for Hot Roll 9/5 Jacks is the same as that for the non-gimmick game. Maybe there's a clue in the fact that 196.94% is about twice the payback for 9/5 Jacks, 98.45%.

You know what we forgot? We have to bet 10 coins per hand. We didn't take that into account in our payoffs. We win 5 coins for Jacks or Better, but we bet 10 coins. The payout per coin isn't 1 but 0.5. We have to divide all of the payouts by 2. Fortunately the Analyzer lets us enter a fractional payout/coin.

When we go back to the calculation screen with the new payoffs, the return is now 98.47%.

Next we set up the parameters the same way we did last week. Choose the # of lines dropdown to change to 10-play.

We get a warning. The macros don't do Risk of Ruin (RoR) calculations for multi-line versions of custom games. We'll have to make believe that our total bet is riding on one line.

That's okay. We're not calculating navigation to the moon and back. We don't have to be exact. Enter 0.25 for Coin Size and 100 for Number of coins to get our bet of $25 per play.

Like last week, let's start with a $1000 bankroll to play four hours at 400 hands per hour. The RoR is 84%. Let's double our bankroll. RoR drops to 66%.

With 10-play 9/5 Jacks last week, $3075 gave us a 5% RoR. I don't get a 5% RoR until the bankroll is about $6500. To get RoR down to 1%, we need to bring about $8000 with us.

The greatly increased bankroll estimates are not surprising. Hot Roll 9/5 Jacks is much more volatile than regular 9/5 Jacks. We have to double our bet and most of the time we don't get anything for the extra coins. But when the multiplier is activated, we get paid at least twice what we would have been paid otherwise. And we may even get paid 12 times the base payout. We might be able to get away with slightly smaller bankrolls at the casino because playing 10-play spreads our risk over multiple outcomes.

The takeaway here is that you need a sizable bankroll to have a low chance of ruin when playing 10-play Hot Roll 9/5 Jacks.

The news tonight reported that the 7-day average for new Covid-19 cases in Clark Country is 396 per day. On March 27, the average was only 281 per day. Last month we celebrated when our test positivity rate fell below 5%, the level at which the virus is considered under control and you can consider loosening restrictions. Our positivity rate climbed steadily in April until it settled in at about 5.7% about two weeks ago.

What do you do given these numbers?

You open up even further on May 1, when capacity limits increase to 80%, social distancing decreases to three feet, and self-service buffets can reopen.

Note that these new rules do not apply to casinos. The Gaming Control Board governs casinos and it said it is going to take into account the number of employees that have been vaccinated in its decision to increase capacity.

Here are the latest figures from https://www.cdc.gov/covid-data-tracker/#cases_totalcases.