| Why Betting Progressions Don’t Work Before I talk about why betting progressions don’t work, I should give you a brief explanation of what they are. A betting progression is a sequence of bets designed to improve the return above that of flat betting. It is a way of placing bets in an exact sequence when winning or losing. The reason it is called a progression is that generally the bets increase, or progress, after a win or loss. If you only follow a sequence of bets when winning and flat bet when losing, you are playing a positive progression. An example is as follows: Initial bet $5 If you win, bet $10 If you lose, repeat the $5 bet If you win the $10 bet, next bet $15 If you lose the $10 bet, return to a $5 bet If you win or lose the $15 bet, return to a $5 bet As long as you are losing, place a $5 bet This is a positive betting progression when winning. In other words your bets are increasing when you are winning. It is also flat betting when losing. You bet $5 every time you lose until you win, then start the winning sequence. If you were to increase your bets when in a losing series of hands, this would be called a negative progression. A negative progression can be as simple as increasing the amount of only one bet. It can also increase two or three bets. Later I will discus them in detail. They are nothing to be afraid of as long as they are limited to just a few strategic increases. Throughout the rest of the book you will see a betting progression shown as a sequence of numbers. The above simple progression would look like the following when expressed in sequence form: $5 - $10 - $15 - $5 - … A betting sequence is commonly expressed in units. The reason is so if you are betting any denomination of unit, you can know what to bet. The above sequence expressed in units looks like the following: 1 – 2 – 3 – 1 - … A player with a $25 unit would bet the sequence: $25 - $50 - $75 - $25 …. A way to know which bet is which is to designate each bet with a symbol preceded with either a W or an L. For instance, W(1) would be the first bet in a winning series. W(5) would be the fifth bet in a winning series. If you see L(3), this would be the third bet of a losing series. A losing series might look like the following: L(1) – L(2) – L(3) – L(4) – L(5) $5 - $5 - $5 - $10 - $20… This will become clearer as you look at the betting progressions that follow later. This concludes the groundwork. Now I will explain why betting progressions don’t work. Many blackjack authors believe betting progressions do not work. They say the player believes in the “Gambler’s Fallacy,” that a win is due. I must admit there are gambling “systems” which are very dangerous such as the Martingale system. This is a negative progression system. Most betting progressions are benign, break even propositions. Dr. Edward O. Thorp stated in his best selling book, Beat the Dealer, that betting progressions are ineffective. “The other betting schemes (i. e. betting progressions) all seemed to have the same flaw (as the martingale). It was no surprise, then when it was later proven, by the mathematical theory of probability that for most of the standard gambling games no betting scheme can ever be devised that will have the slightest effect upon the casino’s long-run advantage.” Kevin Blackwood states: “Every mathematical simulation done on blackjack will tell you the same thing – progressive betting will never make you a winner over the long haul.” Fred Renzey listed betting progressions as an “assumed myth,” since its validity has never been disproved beyond a shadow of a doubt. T. J. Reynolds states, regarding bet-ranging systems: “none is of any real advantage to the player in the long run. Some seem to work better than others in the short term, or under specific playing conditions, but not one is of any benefit financially.” Only Mr. Renzey attempted to show why the progressions don’t work. He used the example of flipping a coin and the possible outcomes. He went on to compute the amount won using a progression and showed there was no difference in the amount won whether using a progression or not. I am going to demonstrate why they don’t work in coin flips and blackjack. Blackjack and coin flipping are two similar games. They both are about 50-50 games. The player who flips a “fair” coin enough times will get 50% heads and 50% tails. In blackjack, if you eliminate the pushes, the percentages are about 47.5% win and 52.5% lose. This will vary depending on the rules of the game. This is based on current Las Vegas rules for a six deck shoe game. Either way, it is close to 50-50. In the coin flip game, regarding wins in a row, you will have heads followed by tails 50% of the time. In other words, if you were betting on heads, you would win 50% of the flips, and 50% of those winning flips would be followed by tails. You will win two flips in a row 25% of the time. You will win three flips in a row, 12.5% of the time, and so on. Because you have a 50% chance of winning each flip regardless of how many flips you won before, the percentage of the times you get a win again is half of the prior percentage. You will get: Heads followed by Tails: 50% of the time Heads – Heads – Tails: 25% of the time Heads – Heads – Heads – Tails: 12.5% of the time. Heads – Heads – Heads – Heads – Tails: 6.25% of the time Heads – Heads – Heads – Heads – Heads – Tails: 3.125% of the time Six Heads in a row – Tails: 1.5625% of the time These are series of wins. The numbers go on down to infinity. I usually lump all wins in a row greater than five together and give them the final 3.125%. Regarding the 50% of losses, or Tails, the percentages are identical. Half of the time with a coin flip you are going to have winning series and half of the time you will have losing series. This is what Dr. Thorp referred to as the Mathematical theory of probability. It might as well be the Mathematical Law of probability. Now I want to look at how much you would win in the coin flipping game when betting a flat bet and what you would win if you use a simple betting progression. When I play Flip The Coin, I bet $5 on heads every time. If I play 100 winning series and 100 losing series, my winning amount may be calculated by multiplying the amount won in each series by the frequency of occurrence. In list form it looks like the following: One win: $5 X 50% = $250 Two wins: $5 + $5 X 25% = $250 Three wins: $5 + $5 + $5 X 12.5% = $187.5 Four wins: $5 + $5 + $5 + $5 X 6.25% = $125 Five wins: $5 + $5 + $5 + $5 + $5 X 3.125% = $79.375 Six or More wins: $5 + $5 + $5 + $5 + $5 + $5 X 3.125% = $93.75 Add them up, and I will win a total of $985.625. This number would be $1000 if I had the patience to type out the table to infinity. How many wins were there? There were 50 single wins, 50 wins in groups of two, 37.5 wins in groups of three, 25 wins in groups of four, 15.625 wins in groups of five, and 18.75 wins of six in a row or greater. These total 196.875 wins, for an average bet of $5 per bet. My losses are identical, because the percentages and bet amount was the same. One loss: -$5 X 50% = -$250 Two losses: -$5 - $5 X 25% = -$250 Three losses: -$5 - $5 - $5 X 12.5% = - $187.5 Four losses: -$5 - $5 - $5 - $5 X 6.25% = - $125 Five losses: -$5 - $5 - $5 - $5 - $5 X 3.125% = - $79.375 Six or More losses: -$5 - $5 - $5 - $5 - $5 - $5 X 3.125% = - $93.75 The losses table looks identical to the win table, and the number of losses also totals to 197. Subtracting my losses of $985.63 from my wins of $985.63, means I won $0 for my efforts. Sometimes when I play Flip the Coin, I use a simple betting progression. I bet $5 for my first bet, and if I win, I let it ride. I now have $10 bet on the second flip. If I win the second time, I pull $5 of my winnings, and bet $15 on the third flip. After three wins in a row, I start the betting sequence over. The fourth bet becomes $5, the fifth will be $10, and the sixth bet will be $15. Again, if I win the $15 bet, I take down my winnings and bet $5. If at any time I lose, I bet $5 until I win, and then begin my sequence again. To see how much I won, I again put it in a list and total it up. One win: $5 X 50% = $250 Two wins: $5 + $10 X 25% = $375 Three wins: $5 + $10 + $15 X 12.5% = $375 Four wins: $5 + $10 + $15 + $5 X 6.25% = $218.75 Five wins: $5 + $10 + $15 + $5 + $10 X 3.125% = $140.625 Six or more wins: $5 + $10 + $15 + $5 + $10 + $15 X 3.125% = $187.5 The total won was $1546.925. Wow! I won a lot more than simply flat betting. Maybe these betting progressions do work after all. Now I am going to subtract my losses, and see what the net profit was. How do I know how much I lost? I can calculate it just as before, but I didn’t lose just $5 each time. Sometimes I lost $10, and sometimes I lost $15. For example, after my 50 solo wins, I bet $10 and lost. Then I flat bet $5 until I won. $10 X 50 = $500 Then, after 25 - $10 wins, I lost $15. $15 X 25 = $375 After I won three in a row 12.5 times, I only lost $5. $5 X 12.5 = $62.50 After four in a row, I again lost $10, 6.25% of the wins. $10 X 6.25 = $62.50 After five wins in a row, I lost $15 again, but only 3.125 times. $15 X 3.125 = $46.875 Finally, I lost $5 for the remaining 3.125% of wins, for another $15.625 lost. Totaled up, my first losses after a winning series are $1062.5. This means my average first loss was $10.625, since there were 100 initial losses after winning series. This was not all of the losses, but only 100 of them. I had 96.875 other losses of $5 each, or another $484.375 lost for a total of $1546.875. This is the same amount that I won, leaving me with a net profit of $0, which is the same profit I had from flat betting. If you need a table to confirm the totals, here it is: One loss: -$10.625 X 50% = -$531.25 Two losses: -$10.625 - $5 X 25% = -$390.625 Three losses: -$10.625 - $5 - $5 X 12.5% = - $257.8125 Four losses: -$10.625 - $5 - $5 - $5 X 6.25% = - $160.15625 Five losses: -$10.625 - $5 - $5 - $5 - $5 X 3.125% = - $95.70 Six or More losses: -$10.625 - $5 - $5 - $5 - $5 - $5 X 3.125% = - $111.328 Now I have the total losses. All I have to do is add these numbers together. Total losses: $1546.87 Total winnings: $1546.925 Looks like I won a nickel, which I must attribute to rounding. This demonstrates that when playing Flip the Coin, there is no benefit in using a betting progression. But, you say, I seldom play Flip the Coin. My primary game is blackjack, and the numbers are different. That is correct. When you play blackjack you win more than even money on splits, double downs, and blackjacks. I can calculate that for you as well. In the above game, when you played flat betting $5, your average bet was..……$5. If I know the frequency of splits, soft double downs, hard double downs, and blackjacks, and the advantage I have, plus the average bet and the total number of bets made, I can tell you how much more you would win when playing blackjack instead of Flip the Coin. I just happen to have a computer program that can tell me both frequency and advantage. I know the average bet, and the total number of winning hands was 197. I obtained the percentages using current Las Vegas rules and a six deck shoe. Splits: Frequency – 4.4% of hands (0.044) Advantage – 5.63% (0.0563) Soft Double Downs: Frequency – 1.6% (0.016) Advantage – 9.045% (0.0945) Hard Double Downs: Frequency – 8.29% (0.0829) Advantage – 18.802% (0.18802) Blackjacks: Frequency – 4.744% (0.04744) Advantage – 143% (1.43) To calculate the total effect, I calculate each individual effect, and add them together. The formula is below: Frequency X Advantage X Average Bet X Number of Wins Splits: 0.044 X 0.0563 X $5 X 197 Wins = $2.44 Soft DD: 0.016 X 0.09045 X $5 X 197 = $1.43 Hard DD: 0.0829 X 0.18802 X $5 X 197 = $15.35 Blackjacks: 0.04744 X 1.43 X $5 X 197 = $66.82 Total of Extras: $86.04 To calculate the “extras” for the betting progression, I must calculate the average bet for the 197 wins. To find the average, I have to divide the total wins, $1546.875, by 197 wins and I have $7.85 for the average win. Substituting this in the formula above, the extras total $135.07. This is looking good. I may have lost the same amount as I won, but the extras pay me more, meaning I win more when I use a betting progression. The answer is still no! The reason is we haven’t finished the calculations. There is one step left to complete. You may remember that the player only wins 47.5% of the hands, and the dealer wins 52.5% of the hands (excluding pushes). This is not a small detail. This is where the house gets its edge. The extras above plus the house edge for that particular game will be taken away by the 5% difference between per cent wins and losses. To calculate this, I am going to need to have the amount won and amount lost. The formula for the calculation is as follows: (%Lost X Total Lost) - ((% win X Total won) + (% win X extras)) / Initial Bet Action = House Advantage Entering our numbers: (52.5% X $985.63) – ((47.5% X $985.63) + (47.5% X $86.04)) / ($985.63) Equals $517.46 – ($468.17 + $40.87) = $517.46 - $509.04 / $985.63 $517.46 - $509.04 = $8.42. $8.42 is lost every 197 hands. The initial bet action is $985.63, so the house advantage is $8.42 / $985.63, or 0.854%. To do the same for the betting progression: (52.5% X $1546.87) – ((47.5% X $1546.92) + (47.5% X $135.07)) / ($1546.87) Equals $812.11- ($734.79 + $64.16) = $812.11 - $798.95 / $1546.92 I lost $13.16 / $1546.92 = a house advantage of 0.851%, virtually identical to the flat betting house advantage. It doesn’t matter which progression you use, the results are going to be the same. There is no advantage to the player in the long run when using a betting progression. The increase in average bet yields higher returns, but they will never offset the increased losses when those progressed bets are lost. The 47.5% win rate and 52.5% loss rate cannot be beaten by any betting progression. |
