blackjack betting strategy

Blackjack betting strategies – computer modeling

blackjack betting strategyI’ve been running some blackjack computer models of different betting systems based on the house winning 52% of the time (following basic strategy, you should fair slightly better).

If you’re going to do positive progression betting (doubling your wager when you win, returning to your base wager if you lose), you should only do it for one progression. If you do it for two progressions, your odds of doubling your money before you bust are only slighly better, and you’ll only get to play 57% as many hands and wager only 72% as much money (earning less player points/comps). You should never do three progressions, as you have a less chance of doubling before busting and will play less hands.

This is my initial mockup of how I was going to visualize the data, and I think it's the best explanation of how to interpret my graphs.
This is my initial mockup of how I was going to visualize the data, and I think it’s the best explanation of how to interpret my graphs.

Based on trying to double a $30 bankroll starting with a $1 base wager, the odds of doubling instead of busting with Positive Progression:

1 progression – graph
percentage = 16.5988
maxhands = 4251
average hands = 377.895254
maxwagered = 5656
average wagered = 500.421616
luck peaks at hand = 120
plateau = $40

2 progessions – graph
percentage = 25.5599
maxhands = 2880
average hands = 214.722045
maxwagered = 4864
average wagered = 361.555029
luck peaks at hand = 47
plateau = $43

3 progressions – graph
percentage = 32.4828
maxhands = 1245
average hands = 119.230565
maxwagered = 2580
average wagered = 245.894373
luck peaks at hand = 34
plateau = $46

4 progressions – graph
percentage = 36.9103
maxhands = 627
average hands = 67.046303
maxwagered = 1622
average wagered = 163.115273
luck peaks at hand = 5
plateau = $45

5 progressions – graph
percentage = 32.7124
maxhands = 88
average hands = 46.695707
maxwagered = 490
average wagered = 132.07771
luck peaks at hand = 5
plateau = $43

6 progressions – graph
percentage = 32.7042
maxhands = 94
average hands = 46.692139
maxwagered = 526
average wagered = 132.049724
luck peaks at hand = 5
plateau = $43

If you’re going to do negative progression betting (where you double your wager when you lose, and return to your base wage when you win), you should only do it for two progressions. This is where you increase your odds by the most and still play a large number of hands with a smaller risk of sudden bust.

Based on trying to double a $30 bankroll starting with a $1 base wager, the odds of doubling instead of busting with Negative Progression:

1 progression – graph
percentage = 16.6742
maxhands = 4700
average hands = 372.467146
maxwagered = 6274
average wagered = 499.200542
luck peaks at hand = 144
plateau = $41

2 progressions – graph
percentage = 26.1289
maxhands = 2554
average hands = 206.209967
maxwagered = 4370
average wagered = 357.574648
luck peaks at hand = 76
plateau = $44

3 progressions – graph
percentage = 34.246
maxhands = 1144
average hands = 110.127216
maxwagered = 2418
average wagered = 237.896454
luck peaks at hand = 52
plateau = $47

4 progressions – graph
percentage = 39.7023
maxhands = 628
average hands = 60.35324
maxwagered = 1600
average wagered = 155.208926
luck peaks at hand = 56
plateau = $50

5 progressions – graph
percentage = 41.1399
maxhands = 395
average hands = 47.503655
maxwagered = 1176
average wagered = 133.371488
luck peaks at hand = 56
plateau = $51

6 progressions – graph
percentage = 41.0399
maxhands = 337
average hands = 47.546197
maxwagered = 1008
average wagered = 133.555192
luck peaks at hand = 56
plateau = $50

7 progressions – graph
percentage = 41.1251
maxhands = 351
average hands = 47.52547
maxwagered = 1128
average wagered = 133.445136
luck peaks at hand = 56
plateau = $51

The graphs indicate the number of hands and whether the session resulted in a bust or doubling of the bankroll, so that you can see the bell curve for how likely you are to bust early. The fewest hands are at the top of the graph, the max hands are at the bottom. The plateau is the bankroll goal that you will have a hard time (less than 50%) chance of surpassing.

Scarily, without a betting strategy, you are more likely to bust your bankroll before doubling it, but you’ll play way more hands and get many more comps.

No betting strategy – graph
percentage = 8.3195
maxhands = 6880
average hands = 625.009406
maxwagered = 6880
average wagered = 625.009406
luck peaks at hand = 260

Please note that the smaller your bankroll and the less you’re trying to increase it, the higher your chances of reaching your goal before busting.

Always plan on busting your bankroll, as you are always more likely to bust than to win money. Depending on whether you’re out to win money (or bust) or to just play lots of hands, it’s up to you on how to bet. The only betting strategy that can give you an advantage (over the long run) is to count cards and bet with the count, and you can’t do this online.

It’s important to only use a bank roll that you plan on losing to the house, to set a goal, and to stop when you reach that goal (or bust).

2 thoughts on “Blackjack betting strategies – computer modeling

  1. Mark,

    Interesting read. Was wondering if you’ve ever looked into blackjack probabilities with stop thresholds lower than 2x. Here’s the setup: $30 bankroll with $1 play using basic blackjack strategy. If your stop threshold was either win $5 or lose $30, how often would you hit +$5 (and then walk away) vs. -$30 (and walk away). The gut says that winning a little then walking is the best strategy, but I’m sure your model can put some math to it. Thoughts?

  2. It is interesting that professionals use computers to model real life problems in just about every field of study, yet when it comes to betting systems computer analysis becomes worthless and unreliable, as the salesman of one system put it. In any event, such an excuse misses the point; the computer runs billions of trials simply to prove that a system is unsound.

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