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Best of John Robison

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Ask the Slot Expert: Risk analysis and video poker

14 April 2021

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.


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

Totals Weekly Increases
US NV US NV
Date Cases  Deaths  Cases  Deaths  Cases  Deaths  Cases  Deaths 
 04/13   31,076,891   559,741   308,343   5,332   480,061   5,321   2,986   57 
 04/06   30,596,830   554,420   305,357   5,275   448,935   7,124   3,084   38 
 03/30   30,147,895   547,296   302,273   5,237   439,510   6,793   939   63 
 03/23   29,708,385   540,503   301,334   5,174   388,928   7,446   1,863   53 
 03/16   29,319,457   533,057   299,471   5,121   381,695   8,362   3,078   81 
 03/09   28,937,762   524,695   296,393   5,040   480,902   11,573   2,413   83 
 03/02   28,456,860   513,122   293,980   4,957   463,356   14,129   2,835   75 
 02/23   27,993,504   498,993   291,145   4,882   451,083   13,923   2,406   162 
 02/16   27,542,421   485,070   288,739   4,720   602,906   21,411   4,149   198 
 02/09   26,939,515   463,659   284,590   4,522   779,305   21,828   5,444   244 
 02/02   26,160,210   441,831   279,146   4,278   1,007,777   22,004   7,249   249 
 01/26   25,152,433   419,827   271,897   4,029   1,312,565   23,385   10,324   250 
 01/19   23,839,868   396,442   261,573   3,779   1,317,119   21,318   11,324   279 
 01/12   22,522,749   375,124   250,249   3,500   1,790,345   22,660   17,217   294 
 01/05    20,732,404   352,464   233,032   3,206   1,499,561   18,435   14,655   233 
 12/29   19,232,843   334,029   218,377   2,973   1,258,540   15,460   12,493   186 
 12/22   17,974,303   318,569   205,884   2,787   1,656,411   18,537   16,472   239 
 12/15   16,317,892   300,032   189,412   2,548   1,494,763   17,247   18,825   229 
 12/08   14,823,129   282,785   170,587   2,319   1,375,502   15,483   18,418   175 
 12/01   13,447,627   267,302   152,169   2,144   1,114,175   10,286   15,942   121 
 11/24   12,333,452   257,016   136,227   2,023   1,197,199   10,784   14,130   106 
 11/17   11,136,253   246,232   122,097   1,917   1,099,790   8,501   11,115   65 
 11/10   10,036,463   237,731   110,982   1,852   767,645   6,838   8,868   68 
 11/03   9,268,818   230,893   102,114   1,784   588,207   5,809   5,936   35 
 10/27   8,680,611   225,084   96,178   1,749   492,026   5,585   5,238   (10) 
 10/20   8,188,585   219,499   90,940   1,759   401,037   5,053   4,501   48 
 10/13   7,787,548   214,446   86,439   1,711   351,270   4,886   3,910   48 
 10/06   7,436,278   209,560   82,529   1,663   306,965   4,962   3,232   36 
 09/29   7,129,313   204,598   79,297   1,627   303,616   5,136   3,058   54 
 09/22   6,825,697   199,462   76,239   1,573   288,070   5,370   2,196   82 
 09/15   6,537,627   194,092   72,043   1,491   250,265   5,404   1,825   65 
 09/08   6,287,362   188,688   72,218   1,426   282,919   5,638   2,734   92 
 09/01   6,004,443   183,050   69,484   1,334   251,790   5,291   3,237   104 
 08/25   5,752,653   177,759   66,247   1,230   330,411   7,889   4,076   125 
 08/18   5,422,242   169,870   62,171   1,105   358,071   7,463   4,973   114 
 08/11   5,064,171   162,407   57,198   991   365,353   7,203   5,776   117 
 08/04   4,698,818   155,204   51,422   874   418,683   7,532   7,367   109 
 07/28   4,280,135   147,672   44,055   764   460,996   7,042   7,130   91 
 07/21   3,819,139  140,630  36,195  674  463,682  5,395  8,181  57 
 07/14   3,355,457   135,235   28,744   617   422,861   5,102   5,607   57 
 07/07   2,932,596   130,133   23,137   560   351,367   3,394   5,006   24 
 06/30   2,581,229   126,739   18,131   536   278,941   6,406   4,367   26 
 06/23   2,302,288   120,333   13,764   510 
John Robison

John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

You may hear John give his slot and video poker tips live on The Good Times Show, hosted by Rudi Schiffer and Mike Schiffer, which is broadcast from Memphis on KXIQ 1180AM Friday afternoon from from 2PM to 5PM Central Time. John is on the show from 4:30 to 5. You can listen to archives of the show on the web anytime.

Books by John Robison:

The Slot Expert's Guide to Playing Slots
John Robison
John Robison is an expert on slot machines and how to play them. John is a slot and video poker columnist and has written for many of gaming’s leading publications. He holds a master's degree in computer science from the prestigious Stevens Institute of Technology.

You may hear John give his slot and video poker tips live on The Good Times Show, hosted by Rudi Schiffer and Mike Schiffer, which is broadcast from Memphis on KXIQ 1180AM Friday afternoon from from 2PM to 5PM Central Time. John is on the show from 4:30 to 5. You can listen to archives of the show on the web anytime.

Books by John Robison:

The Slot Expert's Guide to Playing Slots