simple math advantage

You decide.

PlayerxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxDealer
chance of winning any hand 47%xxxxxxxxxxxxxxxxxxwinning 53%
ignoring pushes

Chance of winning 7 hands in row .005%xxxxxxxxxxxx8.3 hands in a row .005%

Player bets winning progression of $15, $45, $45, $75 till loss then starts at $15

Player's streak xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx dealer's streak
bank bet in circle xxxxxxxxxxxxxxxx
1) -15 15 30 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx-15

2) -30 45 90 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx-15

3) 15 45 90 xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx-15

4) 30 75 150xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx -15

5) 105 75 150xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx-15

6) 180 75 150xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx-15

7) 255 75 150xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx -15

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 8) -15

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 8.3) -4.5

total win $405xxxxxxxxxxxxxxxxxxxxxxxxxxxxxtotal loss $124.5

Mathematically 1 in 200 hands will be in a streak of 7 for the player
1 in 200 hands will be in a streak of 8.3 for the dealer

While your waiting for the streak with basic strategy depending on house rules the odds slightly favor the house.

193 hands @ average $45/hand = 8685 x .02 = $173.70

player wins $405................................dealer $298.20

Does the math add up?

Nope. No progressions can overcome the house edge. There are several threads on the site showing the math of why, try do a search.

Plus the math is just wrong. As I posted on the other thread on this subject, you will lose 7 in a row after only 135 hands not 200. That is with a 48% win percentage that you suggested over there.

Saying progression betting fails or works does not make it so. I searched some threads and have yet to find some analysis other than the statement progression betting will not work. Please refer to a specific thread so I can read what you're talking about. As for the math being wrong, are you talking about multiplication mistakes or the assumptions such as that the win percentage for basic strategy is 47% for the player? I appreciate the input. I would just like to find a way to win and share it with others.
There are variations in statisical probability. But, it would seem in a large sample that with the statistical probability of the player winning 7 in a row and the dealer winning 8.3 in a row being equal, these events would happen many times with the player coming out on top.

My reply double posted, so this is just intended to delete it.

If you could just use a progression system to beat blackjack then everyone would beat it. Common sense should tell you it's not that easy.

I've heard (never counted it myself) that 100 hands per hour is ballpark for blackjack play. The progression systems involve big bets that only result in small profits, often just one unit, as you progress through them.

Any of the experience players will tell you that losing 7 hands in a row, while seemingly very improbable, is only a matter of time and will happen much sooner than you think.

The other key is table limits. If you keep doubling your bet (or doubling +1 unit) to recoup your losses, eventually you will hit that losing streak that reaches the table limit. Then you will end up with a loss of as much as $1000-$2000 on your last hand and be unable to double up again to recoup your losses.

Don't be lazy. Learn a counting system that will give you the long-term advantage, not the casino.

Knox just read the thread about number of hands to win 7 in a row. So we are all on the same page. I used 47% odds of a player winning a hand. To get the probability of more than 1 event we multiply the events so .47 x .47 x .47 x .47 x .47 x .47 x .47 = .0050661 to convert that to 1 out of x hands 1 / .0050661 = 197.39 hands. So at 47% player win percentage the odds of a 7 in a row win streak are 1 out of 197.39 hands. At a 48% player win percentage the odds of a seven in a row win streak are 1 out of 178.5. Also the more often that this event occurs the more money the player will make.

Knox thanks for your interest. There is no doubling. Table limits are not a factor. The progression is bet 15 win, bet 45 win, bet 45 win, bet 75 till you lose. If you lose at any point you start over at 15. Or 1 - 3 - 3 - 5 playing basic strategy. I understand that the dealer will win 7 in a row. Above I calculate the odds of the dealer winning 8.3 times in a row because that equals the probability of the player winning 7 times in a row. If you play 100 hands per hour this should occur once every 2 hours of play. I agree with your common sense remark but maybe that is why most people just say progression betting is no different than flat betting.

Here you go:

http://www.blackjack-scams.com/html/prog__systems.html
http://www.bj21.com/bj_reference/pages/10537.html
http://www.bjmath.com/bjmath/progress/prog1.htm (Archive copy)
http://www.bjmath.com/bjmath/progress/prog2.htm (Archive copy)
http://www.bjmath.com/bjmath/progress/progloss.htm (Archive copy)
http://www.bjmath.com/bjmath/progress/bootmm.htm (Archive copy)
http://www.bjmath.com/bjmath/progress/prog.htm (Archive copy)
http://www.bjmath.com/bjmath/progress/unfair.htm (Archive copy)

And one of our own recent additions:
http://www.blackjackinfo.com/bb/showthread.php?t=2488

-Sonny-

Excellent articles thank you very much.

If you understand the fact that you are at a disadvantage playing only basic strategy, you don't even need to understand the math. No matter what you bet, you will expect to lose money. Previous results or bets do not affect the next hand.

Without investing too much more time in this, I thought the point was the system failed if you lost (not won) 7 hands in a row. So .53 x itself 7 times, just like you did above, is 1.17%. 1/1.17% is even worse, that is one in 85 hands!

On the flip side, any system that depends on winning 7 hands in a row is also doomed to failure, unless it only has to happen once within the number of hands you mentioned above. I am sorry to say such a system does not exist.

In game where next outcome does not depend on the last outcome, the odds never change, and the betting amount therefore doesn't matter.

Non of these progression systems work. Even if card counting progressing when you have the advantage isn't even optimal.

The optimal bet in a win/loose 2:1 game is always win% - loose%. So in the case of blackjack at 3% house edge it is -3%, ie. You can bet upto 3% of all your money as the dealer.


Having said that blackjack is not a game where the bast results do not affect the next hand. Card counting aside on average after a win you are 0.10% less likly to win the next hand, after a push you are 0.15% less likly to win and after a loss you are 0.1% more likly to win. In most games the house edge is 0.5% you can simply wait for 6 losses in a row then increase your bet and MAYBE you will get ahead by 0.1%