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Backwards Kcajkcalb

9 November 2001

By Walter Thomason

Steve Bourie and I were sitting in the lounge of a casino gaming ship, waiting for our "comped" BLT sandwiches. Steve is the author of American Casino Guide, a neighbor, and a gambling buddy.

We weren't happy. We had just completed a four-hour cruise, and both of had lost at the blackjack tables.

Steve said, "The Wally System didn't work." (The Wally System is his name for my Four-Step Positive Progressive betting system.)

I replied, "Well, your wonderful counting system didn't work either! And the cards just weren't going my way tonight."

"Yeah," he said. "Maybe you lost because the wins and losses occurred at the wrong time... Maybe you should have played all the hands backwards. But, according to your theory, you don't raise the bet because you expect to win the next hand; you only raise the bet if you won the previous hand. So, reversing the order of the hands shouldn't make any difference, right?" (Steve really talks like this.)

"Right... I think," I replied. Frankly, I was caught off guard by Steve's attempt to trap me into saying something stupid (his favorite pastime), and quickly changed the subject.

But his question got me thinking. What happens when the consecutive order of wins and losses is completely reversed? The flat bettor, one who bets the same amount on every hand, would obviously be unaffected by this reversal since his bet is always the same. But would a player using my progressive system have the same results? Or could a losing session turn into a winning session (or vice-versa) if the order of the hands was reversed? [Note: Don't ask why I think about stuff like this...It's an illness.]

To answer this question, I calculated the win/loss results for Player #1 and Player #2 for the first 75 shoes in Bob Hubby's book, Blackjack Tracker. This book presents the win/loss results for over 50,000 consecutively dealt hands, and is an excellent tool for conducting comparative analyses. It is not a list of simulated hands but real-world, manually dealt hands.

The first step was to calculate the net win/loss amount for Players #1 and #2, and compare them to the flat bettors results for the same 75 shoes:

Progressive Bettor #1 = Won: $1,565
Flat Bettor #1 = Won: $1,305
Progressive Bettor #2 = Lost: $315
Flat Bettor #2 = Lost: $1,110

For this study the progressive players used my 4-Step system ($20, $30, $40, $50 per hand), and the Flat Bet players bet $30 per hand. The average bet for all players was approximately the same, as were all other game rules and strategies. The only difference between the two types of players was how they chose to bet on each hand.

The results of this initial comparison -- the progression beating the flat-betting option -- did not surprise me, and is supported by my previous research [see my book, Twenty-first Century Blackjack].

But what happens when the order of the wins and losses is reversed? Would the flat or progressive players' results be seriously altered?

As expected, the flat bettor's results were the same regardless of the order of wins or losses, because they each made the same initial bet at the start of each hand, and this bet was never changed as a result of the outcome of previous or future hands.

Not so with the progressive bettors. The normal pattern would be to start each new shoe with a $20 bet, increase it by $10 for each net win to a maximum of $50, then drop to the initial $20 bet after a net loss on a hand. I reversed the pattern by starting with the last hand in the shoe as my initial $20 bet, played the shoe backwards, and ended up with what was previously the first hand in the shoe.

The final results for both progressive and flat bettors, when the win/loss order was reversed, is as follows:

Progressive Bettor #1 = Won: $1,595
Flat Bettor #1 = Won: $1,305
Progressive Bettor #2 = Lost: $265
Flat Bettor #2 = Lost: $1,110

As you can see, Progressive Player #1 won $30 more, and Progressive Player #2 lost $50 less by playing the shoes backwards! Collectively the two flat bettors made a net profit of $195 for 75 shoes of play, regardless of the order of the wins and losses. Collectively the progressive players made a net profit of $1,250 when the hands were played in their normal order, and a net profit of $1,330 when the order of the hands was reversed!

So what's the point of all this? Actually, there are several points:

  1. Flat bettors are unaffected by the order in which wins or losses occur, and can only show a profit if they win more hands than they lose, which is not normally the case in the long run. With the 75 shoe sample that we analyzed, the two flat bettors collectively made a net profit of $195 after about 2,400 hands of play; not bad considering long-term "expected" results would show a loss.
  2. The progressive bettors, using my system, won much more than the flat bettors, although the average bet for all four players was about the same. Even though "risk per hand" was about the same, the progressive bettors won more than six times as much as the flat bettors, regardless of whether the shoes were played forwards or backwards.
  3. Regardless of the betting system employed, Player #2 lost money, illustrating that neither system wins consistently in the short run. Likewise, Player #1 won money with either of the betting systems employed.
  4. Back to the original question that prompted this research: "Does reversing the order of wins or losses seriously alter the results of play?" Based on this limited study, the answer appears to be no. Neither player was seriously affected by the order of the wins or losses, but the progressive players maintained a better track record than the flat bet players in either direction. "Bad" shoes hurt each player; "good" shoes helped each player. But the progressive bettor seems to be helped more by good shoes and hurt less by bad shoes than is the flat bettor.

Final note: All of the data presented above can be duplicated and verified by anyone, simply by using Bob Hubby's book Blackjack Tracker. Write to him at 760 Country Club Road, Corydon, IN 47112.


For more information about blackjack, we recommend:

21st Century Blackjack: New Strategies for a New Millennium by Walter Thomason
The Ultimate Blackjack Book by Walter Thomason
Best Blackjack by Frank Scoblete
The Morons of Blackjack and Other Monsters! by Frank Scoblete
Winning Strategies at Blackjack! Video tape hosted by Academy Award Winner James Coburn, Written by Frank Scoblete
Walter Thomason
Walter Thomason is the best-selling author of Blackjack for the Clueless and the editor of The Experts’ Guide to Casino Games and The Ultimate Blackjack Book.

A long-time casino gaming enthusiast, he is a frequent contributor to
The New Chance and Circumstance, Midwest Gaming & Travel, and Heartland Casino News.

His new book is
21st Century Blackjack: A New Strategy for a New Millenium. He can be reached
at PO Box 550068, Ft. Lauderdale, FL 33355.

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