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Ask the Slot Expert: An unusual video poker experience?

29 September 2021

Question: Had a very interesting 7-hour triple-double video poker session (25 cents per hand) yesterday at the local Indian casino. Ended the session with gross winnings of $1,020, and no royals (had one the previous 5-hour session).

I would think that is a bit unusual.

What do you think?

Answer: We can actually calculate how likely it is. I have done it to create graphs that show the distribution of returns after playing a certain number of hands. Don Catlin told me that I could call the process "convolution". This process is pretty convoluted.

Here's how it goes. The outcome of our first hand can be one of only a certain number of outcomes -- royal flush, straight flush, full house, nothing, etc. For Triple Double Bonus, there are 14 possible outcomes. We know the probability of achieving each outcome and we know how much each outcome pays.

If we drew a diagram of what could happen, we have a starting node. Then we have a line to the royal flush node and its 4000-coin payoff and we have a very small probability that we follow that path. Another path takes us to a flush and we have a much higher probability to follow that path. For Hand 1, we have a node for each outcome and the probability of following the path to that outcome.

Let's say we got a royal for Hand 1 (Yippee!!). What are the possible outcomes for Hand 2?

All 14 outcomes are possible and we know the probability of following the path to each outcome. There's a really small probability we follow the path to the second royal. So there's a really, really small probability that we follow the path to a royal on Hand 1 and a royal on Hand 2. There's a much greater probability that the next step will be to a nothing hand.

If there are 14 possible outcomes for each hand, the total number of distinct paths is 14 raised to the number of hands played. We go from 14 to 196 to 2744 to 38,416 to 537,824, and so on. The number of distinct paths gets really big really fast.

Fortunately, we can limit the amount of data we have to deal with. First, we don't care about distinct paths, only how much we've won. We don't care how we ended up on the +10 coins node at the end of Hand 2, for example. It could be either two Jacks or Better, two Two Pair, one of each, or 3-of-a-Kind and nothing. We need only one +10 node at Hand 2. The probability of reaching it is the sum of the probabilities of getting these hands:

Jacks or Better - Jacks or Better
Two Pair - Two Pair
Jacks or Better - Two Pair
Two Pair - Jacks or Better
3-of-a-Kind - Nothing
Nothing - 3-of-a-Kind

I think that's all of the ways a Triple Double Bonus machine could have paid you 10 coins after two hands. Note that on each line you multiply the probabilities together and then add up the products.

We can eliminate many paths by combining all of the paths that lead to the same number of coins paid to us.

The second way to decrease the number of paths to track is to, let's say, cull the herd. One way to do that is to eliminate nodes whose probabilities fall below a threshold level. There's no reason to maintain a royal-royal-royal-royal-... path because the probability of getting a royal on every hand is small.

Another way to cull the herd is to decide how many nodes to pass from one hand to another -- like 1000, 5000 or 10,000 -- and sort the nodes by likelihood and drop the least likely nodes that don't make the cut.

When we're done playing the number of hands we want to play, we can graph the data. The value of each node is the x-axis and the probability of getting to the node is the y-axis. We end up with graphs that look the ones on this page, which is where I got the idea to create graphs for the games that I play.

I made my graphs about 20 years ago, long before I moved to Las Vegas. I didn't make one for Triple Double Bonus. I don't play it because it's too volatile. I did look at a strategy chart for it because it used to be one of the best paytables offered at Suncoast, but I was put off by how complicated the strategy is.

I have played TDB occasionally just to see if I could hit something big. I had won a good amount of free play in some sort of promotion a few years ago, so I decided to see if I could turn it into something big playing quarter TDB. I played for a little while before hitting four aces. That's something big. I was happy.

I watched the credit meter increment. It didn't stop after adding $200. Let me take a closer look at the hand.

I had four aces with a kicker. A grand. Now, that's really something big and an excellent outcome for my free play.

You ended up about $1000 ahead too. But you did it playing nickels. You said you also did not get a royal, but you didn't mention anything about how well you did with quads. I imagine you must have hit quite a few of them.

I agree with you. Your experience was unusual. But you're better qualified to rule on the matter than I am because I don't play TDB. How frequently have you ended up $1000 ahead?

To quote a lyric from a song by Premiata Forneria Marconi out of context, "Sometimes your oyster holds a pearl."


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 
 09/28   43,051,429   689,534   418,477   7,045   817,218   14,463   6,160   165 
 09/21   42,234,211   675,071   412,317   6,880   971,637   14,691   7,466   152 
 09/14   41,262,574   660,380   404,851   6,728   1,176,763   12,919   10,256   145 
 09/07   40,085,811   647,461   394,595   6,583   975,725   10,076   5,237   104 
 08/31   39,110,086   637,385   389,358   6,479   1,113,414   9,385   7,592   173 
 08/24   37,996,672   628,000   381,649   6,306   1,045,491   7,507   8,117   116 
 08/17   36,951,181   620,493   373,649   6,190   959,978   4,715   7,065   150 
 08/10   35,991,203   615,778   366,584   6,040   819,524   3,987   7,652   122 
 08/03   35,171,679   611,791   358,932   5,918   622,832   2,279   7,489   81 
 07/27   34,548,847   609,012   351,443   5,837   652,251   2,394   8,347   79 
 07/20   33,896,296   606,618   341,096   5,758   169,933   1,478   3,351   28 
 07/13   33,726,363   605,140   339,745   5,730   181,047   1,959   4,982   33 
 07/06   33,545,316   603,181   334,763   5,697   75,104   1,373   2,234   27 
 06/29   33,470,212   601,808   332,529   5,670   87,507   2,057   3,020   24 
 06/22   33,382,705   599,751   329,509   5,646   75,420   2,157   1,930   22 
 06/15   33,303,285   597,594   327,579   5,624   95,797   2,293   1,560   17 
 06/08   33,207,488   595,301   326,019   5,607   114,250   3,762   2,271   21 
 06/01   33,039,238   591,539   323,748   5,586   123,333   3,709   991   27 
 05/25   32,969,905   587,830   322,757   5,559   174,125   4,234   1,676   26 
 05/18   32,795,780   583,596   321,081   5,533   223,966   4,230   2,301   27 
 05/11   32,571,814   579,366   318,780   5,506   303,856   4,687   2,541   33 
 05/04   32,267,958   574,679   316,239   5,473   343,348   4,908   2,559   40 
 04/27   31,924,610   569,771   313,680   5,433   383,163   4,958   2,747   65 
 04/20   31,541,447   564,813   310,933   5,368   464,556   5,072   2,590   36 
 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