Playing 3 hands at once at the BJ table

     Is it just me or is this inviting disaster?  Maybe I'm always expecting the worst...watching a player be dealt a 12, 15 and 17.  Or if they do get a 19, 20 and 20, dealer will end up with 21.  

     Since there seem to be statistics for everything else in blackjack, does anyone have an idea what odds are of winning playing 3 hands at once?  Ironically I see this happen quite a bit at the $50 and $100 tables.

                 Tim

Playing 3 hands doesn't increase or decrease your chances of winning. What it does is "spread out" the results, compared to playing only one hand in a given round.

Since the player's win percentage is less than half--the player wins 44% of the time, loses 48%, and pushes the rest, the numbers aren't tidy, but I can give you a rough idea. Let's say that you're playing a game, blackjack or something else, where the player wins half the time. The chances of winning one hand are 1/2. The chances of winning two hands are 1:in 4. The chances of winning three hands are 1 in 8.

Now, if you played three hands at once in this gamen, 1 out of 8 times, you would win all three; 1 of 8 times, you would lose all three; 3 out of 8, you would win 2, lose 1; and 3 out of 8, you would win 1, lose 2.

Since the player loses somewhat more than half the time in actual blackjack, his chance of losing all three bets is roughly 1 in 7, disregarding pushes. That's obviously much lower than the chance of losing a single bet.

Playing 3 hands doesn't increase or decrease your chances of winning. What it does is "spread out" the results, compared to playing only one hand in a given round.

Since the player's win percentage is less than half--the player wins 44% of the time, loses 48%, and pushes the rest, the numbers aren't tidy, but I can give you a rough idea. Let's say that you're playing a game, blackjack or something else, where the player wins half the time. The chances of winning one hand are 1/2. The chances of winning two hands are 1:in 4. The chances of winning three hands are 1 in 8.

Now, if you played three hands at once in this game, 1 out of 8 times, you would win all three; 1 of 8 times, you would lose all three; 3 out of 8, you would win 2, lose 1; and 3 out of 8, you would win 1, lose 2.

Since the player loses somewhat more than half the time in actual blackjack, his chance of losing all three bets is roughly 1 in 7, disregarding pushes. That's obviously much lower than the chance of losing a single bet.

Not exactly right, since those three hands aren't exactly independent trials.  There's some correlation between wins on multiple hands; that's a basic principle of tournament blackjack (you can count on a disproportionate number of times when either everyone wins or everyone loses).  So, the odds of winning three simultaneous bets in something like roulette are a bit worse than 1 in 8, but that denominator is likely smaller with three BJ bets.  I have no idea how to calculate it, though (probably best done through a simulation).

Then you see the genius playing 3 hands martingale his losses...

Well, yeah, I didn't delve that deeply into it. Obviously, if you lose one hand to a dealer blackjack, you usually lose the other two as well; if you win one hand due to the dealer busting, you have a better than average chance of winning the other two as well. Then there's the consideration that the average player win on a given hand is more than 1.0 bets, due to naturals, doubling, and splitting.

I simply wished to show that if you play three hands, a net result of +1 or -1 bets is much more likely than +3 or -3. That's probably the appeal. Split your per-hand stake into three bets, and you get more excitement for your buck without increasing volatility.