Blackjack Strategy

[MicroBob]

Someone correct me if I'm doing this wrong:


If you played at a casino with no max-bet and started at $5 and always doubled your bet after each loss:

It would take 15 straight losses to drop $81.9k in a single hand.
and you will have also lost $81.9k in the 14 previous bets to get to this point already for a total of almost $163k lost.

The odds of losing 15 straight hands of blackjack is about 1:25k.

This is assuming about 51% chance of losing the hand (42% win, 9% push) which actually starts to really add-up compared with a 50/50 chance.

At 100 hands an hour (which would be really slow if you were playing the dealer heads-up) you should expect to see such a streak once every 250 hours I believe.

So if you played 40 hours a week doing this martingale system (base of $5 and doubling after each loss) then you should expect to have a 15-hand stretch where you drop $163k-ish 1 time every 6 weeks or so.


Chances of dropping $163k in a 15 hand stretch is significantly less than chances of getting dealt a pocket-pair 4 hands in a row.


If you got to that point and still wanted to keep going it would only take 3 more losses to reach 1.3-million in total losses.
This is about 1:200k which is less than your chances of flopping a royal.

[Sandra Bullett]

BJ is not the mathematically easiest game to do Martingale scenarios in, for two reasons:

1) The chance of a win is 46%, chance of a loss 54%, assuming that pushes are simply ignored and another hand played with an unchanged bet, because what else could you do? (MicroBob, your saying a 51% chance of loss is incorrectly giving pushes some value, but they have no effect on the Martingale progression and have to be ignored and replayed). (Also, my BJ days are long over, my memory of the chance of a non-push hand losing being 54% might be wrong, but I think not). A 54% chance of losing is quite different from a 50% chance (not that any casino games offer that). The chance of 15 losses in a row with a 54% chance of losing is 3.2 times higher than with a 50% chance of losing (and 2.4 times higher than your 51%)

2) Many BJ hands are not even-money propositions. If you get a blackjack, you're paid 3:2, so how do you account for that? (assuming the chance of a blackjack is 1-in-21, there's almost exactly a 50% chance of getting at least one within the 15 hands you are proposing). Even worse for hands that offer splits or doubles (or both). These extra bets might win or lose. If they lose, for example, do you quadruple your next wager? Given that, from memory, about 12% of BJ hands are split or doubled (I am very hazy on that number, might be otherwise, but should be similar), again it is likely that your 15 hand sequence will get messed up.

But otherwise your mathematics are fine (although, as I say above, the chance of a 15-loss streak is 2.4 times more than you use (ignoring pushes).

Using equally likely poker examples is a good idea (we've all had successive hands with pocket pairs, so know that does happen enough so that if we had $163k riding on the outcome, we'd be a bit nervous).

[MicroBob]

I looked at my percentages and realize it adds up to 103%.
Not good.

But I'm pretty sure it's something close to that (depending on the game of course).
I now think it's something like 42-50-8 or 41-50-9.
Something like that.
I'm going off memory here and don't feel like digging through my old BJ books to try to find it.

Regardless, your point that the push shouldn't be counted is a valid one.

My calculations pretty much did it for a 15-loss streak with no pushes in there.
But for most who were to try this system they would just stay at the same bet-size after a push.

So a 17 hand streak with 15 losses and 2 pushes would be the exact same as 15 straight losses with 0 pushes. But my calcs were ONLY for 15 losses and 0 pushes.

your theory that we should ignore the pushes and make it more of a 46/54 proposition is clearly the way it should be done.


I found it somewhat interesting that 15 straight hands at 50% is 1:31k while 15 straight hands at 51% is 1:25k.


You are correct that it's about 2 1/2 times more likely at 54%.

I just looked at 15 straight occurances at 54% and landed on close to 1:10k.


So at a snail's pace of only 100 hands an hour playing 40 hours a week you will have such a $163k loss roughly once every 2.5 weeks.


Obviously most people in live casinos who are actually trying such a martingale system would get stopped long before then by betting maximums or bankroll considerations.

Low-rolling casino I dealt at for 8 months has a $500 max-bet limit and I'm not sure they would be willing to raise it for you.


For a more realistic bankroll of $10k (still probably more than many martingalers are using) it would only take 11 losses to bust you.
This is a 1:1000 shot (if 54% chance of losing a hand).

at just 100 hands an hour you should expect to have a $10k downswing once every 10 hours or so.


At the casino i used to deal at with a $500 max-bet you will not be alloed to place the bet you nee after only 7 losses.
(5, 10, 20, 40, 80, 160, 320...next bet would need to be 640)

Chance of you sitting down and losing 7 straight hands of blackjack (at 54%) = 1:100

[Sandra Bullett]

My post about the interest earning rates was not entirely pointless. The bankroll required to play a Martingale for any reasonable period of time (long enough to make ruin unlikley for at least several weeks) is so large that it would earn more (with no risk of losing) if you simply put it in the bank.

Any gambling "strategy" which is beaten by depositing money in the bank is desperately in need of some refinement.