Will You Lose More When Using A Limited Negative Progression?

If you were to read a blackjack book with a card counting emphasis, you will find them railing about how dangerous negative progressions are.  Then they will give the Martingale as an example.  I too rail against the Martingale, but the Martingale is the most extreme example of a negative progression.  What I and a few other authors promote is a limited negative progression of one, two or even three bets.  Popik’s limited negative progression increases the one unit bet to a two unit bet in the L4 position.  The L4 position is the bet placed after three losses in a row.  In units, the progression is as follows:

L(1)  L(2)   L(3)    L(4)    L(5)
1        1       1         2        1

This may seem like no big deal.  It certainly doesn’t look dangerous to me.  It is only one unit.  It’s not going to break anybody’s bank.  Yet, when you do the math, it makes a significant contribution to the bottom line.  Popik found there was a slight advantage if this bet is made.  

Now, look at E-Z Bet Conservative negative progression:

1 – 1 – 1 – 2 – 4 – 1 …

This betting sequence was developed from a table of the frequency of losses in a row.  The only difference between it and Popik’s sequence is the L5 bet is increased by 3 units.

You might say, “All the experts say it is foolish to raise one’s bet when losing.”  In the next sentence they say it makes no difference if you vary your bets when you are winning.  Actually, if it doesn’t cause you to win more to play a positive progression, then it shouldn’t cause you to lose more when you play a negative progression.  They can’t have it both ways.

So, let’s find out once and for all.  To calculate if they are the same I will use the following generic percentages of losses in a row.

You will have:
One loss followed by a win 50% of the losing series
Two losses followed by a win 25% of the losing series
Three losses followed by a win 12.5% of the losing series
Four losses followed by a win 6.25% of the losing series
Five losses followed by a win 3.125% of the losing series
Six or more losses followed by a win 3.125% of the losing series

These percentages are pretty close to the actual  percentages found once you run blackjack simulations.

Now, if I flat bet a $5 unit, I can calculate how much I would lose after the series of loses followed by the initial bet won (W1).  When flat betting W1 will always be one unit, but later you will see it vary with a negative progression.  The following is the net amount lost after 100 series of losses:

-$5 + $5 = $0 X 50 = 0
-$5 -$5 + $5 = -$5 X 25 = -$125
-$5 - $5 - $5 + $5 = -$10 X 12.5 = -$125
-$5 - $5 - $5 - $5 + $5 = -$15 X 6.125 = -$93.75
-$5 - $5 - $5 - $5 - $5 + $5 = -$20 X 3.125 = -$62.50
-$5 - $5 - $5 - $5 - $5 - $5 + $5 = -$25 X 3.125 = $78.125

Total:                                                         
- $484.375      

This is the net loss after 100 series of losses followed by a win.  Now I’m going to do the same thing using the E-Z Bet Conservative negative progression.

-$5 + $5 = $0 X 50 = 0
-$5 - $5 + $5 = -$5 X 25 = -$125
-$5 - $5 - $5 + $10 = -$5 X 12.5 = -$62.5
-$5 - $5 - $5 - $10 + $20 = -$5 X 6.25 = -$31.25
-$5 - $5 - $5 - $10 - $20 + $5 = -$40 X 3.125 = -$125
-$5 -$5 -$5 -$10 -$20 -$5 +$5 =-$45 X 3.125 = -$140.625

Total:
-$484.375

As you can see, the amount lost is exactly the same.  You can put any number in any position and the outcome will be the same.  So, does this look dangerous?  Or foolish?   No it isn’t any more dangerous than flat betting, it’s just different.  So, you ask, why do it?  There are three reasons to do it.  

1. You raise the average bet.  You will recall that if the average bet is raised, the return from Blackjacks, double downs, and splits is raised as well since the return is directly proportional to the average bet.

2. If you play during periods when the dealer doesn’t have very many long winning streaks, i.e. no more than 4 dealer wins in a row, you average losing only one half unit per loss compared to one unit when flat betting.

3. Is it adds a little excitement to the losing series.  If you have a four unit bet out and receive a blackjack, that’s more exciting than with a one unit bet.

A way of looking at it is you don’t lose any more than flat betting, but you have a lot to gain.