June 20th, 2012 at 5:59:38 AM
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Hello,

I've been testing seven classic betting systems for blackjack with my blackjack simulator. Three types of games have been tested:

-1.000.000 long games (one hour playing, 70 hands)

-1.000.000 short games (about 15 min playing, 20 hands)

-100.000 games playing for a target bankroll (150% of initial bankroll)

Each game started with bankroll=200 and betting unit=5, under these rules:

-Blackjack pays 3 to 2, 6 decks, penetration 70%, Dealer stands on soft 17, Resplitting allowed, Doubling after split allowed, Hitting aces after split not allowed. Insurance taken when true count>= +5

-Minimum bet 5, maximum bet 500

-5 players, main player in second position (this really doesn't matter)

For cancellation system, the most conservative line "1" was used. For Paroli, the player duplicates bet after a win (anti-martingale), returning to one unit bet after three consecutive wins or losing. For counting cards, Hi-low system was used, bet=true count * betting unit if true count positive, otherwise bet=1 unit.

These are the results, ordered by best to worst system based on average final bankroll.

AN HOUR PLAYING (70 hands)

Graphic means that 9,96% of games finished with bankroll between 200-220, 1.17% games finished with bankroll=0 and so on.

An the average of all final bankrolls is calculated.

ABOUT 15 MINUTES PLAYING (20 hands)

PLAYING FOR A TARGET BANKROLL 150%

In this case, the game ends if bankroll>=300 (150% initial bankroll) or if bankroll is not enough to do next bet (bankruptcy or 2,5, since minimum bet=5)

The best systems will be those with more winner games (games that ended reaching target)

CONCLUSIONS

When playing long games, it’s better to bet flat or counting cards. If you can't count cards and want a little more excitement, play Paroli, Oscar’s Grind, or Cancellation. Avoid Martingale or D’alembert.

With long games (not including counting cards) the bigger average bet the worst system, except for Martingale and D’alembert, where both systems have similar results despite the average bet in D’Alembert is slightly higher.

When playing short games, again it’s better flat betting and counting cards, but the order of the rest of systems changes. Here, Paroli is not a good option, on the other hand Paroli is the worst system, despite the average bet is not as high as in Martingale and D’Alembert. I don’t know the mathematical reason.

Again, D’alembert is better than Martingale despite D’alembert average bet is the highest of all systems.

Of course, when playing without counting cards, it’s better to play short games instead long games, the more hands played, the more money lost.

When playing for a target bankroll, then the things are very different. In most systems, results are worse than playing a fixed number of hands, looking average final bankroll. This means that the frequent small wins don’t compensate the occasional big losses. Nor does playing with fixed number of hands, but the difference is bigger.

Not mentioning counting cards, Oscar’s Grind is the winner, better than flat betting (I don’t know the reason)

Also, flat betting is worse than cancellation, D’alembert and Martingale. Paroli is the worst by far.

So, under this configuration, if you are playing for a target bankroll, it’s better to use a Betting System than flat betting.

If this is not true (theoretically), then the only explanation I have is that more tests (1.000.000 instead of 100.000) must be done.

I've been testing seven classic betting systems for blackjack with my blackjack simulator. Three types of games have been tested:

-1.000.000 long games (one hour playing, 70 hands)

-1.000.000 short games (about 15 min playing, 20 hands)

-100.000 games playing for a target bankroll (150% of initial bankroll)

Each game started with bankroll=200 and betting unit=5, under these rules:

-Blackjack pays 3 to 2, 6 decks, penetration 70%, Dealer stands on soft 17, Resplitting allowed, Doubling after split allowed, Hitting aces after split not allowed. Insurance taken when true count>= +5

-Minimum bet 5, maximum bet 500

-5 players, main player in second position (this really doesn't matter)

For cancellation system, the most conservative line "1" was used. For Paroli, the player duplicates bet after a win (anti-martingale), returning to one unit bet after three consecutive wins or losing. For counting cards, Hi-low system was used, bet=true count * betting unit if true count positive, otherwise bet=1 unit.

These are the results, ordered by best to worst system based on average final bankroll.

AN HOUR PLAYING (70 hands)

Graphic means that 9,96% of games finished with bankroll between 200-220, 1.17% games finished with bankroll=0 and so on.

An the average of all final bankrolls is calculated.

ABOUT 15 MINUTES PLAYING (20 hands)

PLAYING FOR A TARGET BANKROLL 150%

In this case, the game ends if bankroll>=300 (150% initial bankroll) or if bankroll is not enough to do next bet (bankruptcy or 2,5, since minimum bet=5)

The best systems will be those with more winner games (games that ended reaching target)

CONCLUSIONS

When playing long games, it’s better to bet flat or counting cards. If you can't count cards and want a little more excitement, play Paroli, Oscar’s Grind, or Cancellation. Avoid Martingale or D’alembert.

With long games (not including counting cards) the bigger average bet the worst system, except for Martingale and D’alembert, where both systems have similar results despite the average bet in D’Alembert is slightly higher.

When playing short games, again it’s better flat betting and counting cards, but the order of the rest of systems changes. Here, Paroli is not a good option, on the other hand Paroli is the worst system, despite the average bet is not as high as in Martingale and D’Alembert. I don’t know the mathematical reason.

Again, D’alembert is better than Martingale despite D’alembert average bet is the highest of all systems.

Of course, when playing without counting cards, it’s better to play short games instead long games, the more hands played, the more money lost.

When playing for a target bankroll, then the things are very different. In most systems, results are worse than playing a fixed number of hands, looking average final bankroll. This means that the frequent small wins don’t compensate the occasional big losses. Nor does playing with fixed number of hands, but the difference is bigger.

Not mentioning counting cards, Oscar’s Grind is the winner, better than flat betting (I don’t know the reason)

Also, flat betting is worse than cancellation, D’alembert and Martingale. Paroli is the worst by far.

So, under this configuration, if you are playing for a target bankroll, it’s better to use a Betting System than flat betting.

If this is not true (theoretically), then the only explanation I have is that more tests (1.000.000 instead of 100.000) must be done.

June 20th, 2012 at 6:40:48 AM
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Thanks for the great work, this definitely helps me to adapt my playing style to my targets.

My favorite bet: Double Down!

June 20th, 2012 at 2:32:25 PM
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deleted

DUHHIIIIIIIII HEARD THAT!

June 20th, 2012 at 2:34:01 PM
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Quote:IbeatyouracesWhy was the card counter waiting until a TC of +5 or higher?

Because he was drunk. Or stupid. Or both.

June 20th, 2012 at 10:40:19 PM
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The card counter was not waiting for anything, but the card counter takes insurance if the true count is high, as it is the normal way of playing blackjack, only taking insurance when count is high because the remaining deck is rich in high cards.

June 24th, 2012 at 4:16:48 AM
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The counter should have taken insurance at +3, though.

June 24th, 2012 at 5:53:08 AM
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deleted

DUHHIIIIIIIII HEARD THAT!

July 1st, 2012 at 4:12:53 PM
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Thanks for all your hard work regarding playing systems, THANKS!!!!

Ken

Ken

July 3rd, 2012 at 6:14:18 AM
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You're welcome.

Now I'm thinking about doing the same test for rich gamblers, playing with a very high bankroll, but I think there will be fewer differences between the systems. So, perhaps this test is not worth.

Another test that I would to do is to find the minimum bankroll to play each system with no risk of bankruptcy during an hour.

About the insurance, I'll test it, because I' ve read different versions of how the true count should be for taking insurance or not.

I was thinking that in order to make the test more accurate, the player should allways bet flat. Counting cards would not change the wagger, but only would be considered to take insurance or not. I don't know if this is a good idea or not, because the insurance bet depends on the main bet .

Of course I know that the true count also influences the basic strategy, for example if TC is high, stand 12 against a dealer's 2 instead of hitting. But my program can not do that kind of dynamic variations to basic strategy while playing.

Now I'm thinking about doing the same test for rich gamblers, playing with a very high bankroll, but I think there will be fewer differences between the systems. So, perhaps this test is not worth.

Another test that I would to do is to find the minimum bankroll to play each system with no risk of bankruptcy during an hour.

About the insurance, I'll test it, because I' ve read different versions of how the true count should be for taking insurance or not.

I was thinking that in order to make the test more accurate, the player should allways bet flat. Counting cards would not change the wagger, but only would be considered to take insurance or not. I don't know if this is a good idea or not, because the insurance bet depends on the main bet .

Of course I know that the true count also influences the basic strategy, for example if TC is high, stand 12 against a dealer's 2 instead of hitting. But my program can not do that kind of dynamic variations to basic strategy while playing.