Help me on the math...

Living in Colorado now, and the casinos here have a game called "Blackjack Streak," which may .. or may not .. be beatable.

First, the explanation. State law in Colorado says the max bet on a BJ hand is five bucks -- which is also the minimum bet. But the casinos devised a way around it by letting you bet five consecutive hands, anywhere between one and five dollars, as well as the "primary" hand. Hence, the name "Streak."

Beat the dealer five straight times, the fifth bet pays off at LOTS to one. The second pays three to one, the third 8 to 1, and the fourth and fifth bets .. I forget, but they're healthy payouts.

All bets are made on the same circle (the consecutive bets go into smaller circles above the main circle). A push on one hand is a push on all Streak bets. End of the shoe doesn't mean you lose your Streak bets, but you can take them back.

I'm a decent counter who is smart enough to avoid "SuperDumb 21" and 6-5 naturals, but .. I need some help here. Six deck shoe, assume decent penetration (it's usually not bad) up here.

Someone help me with the math. Is the game beatable, and .. if so .. how does one calculate the EV/"counting" tables?

Colorado isn't listed in CBJN, so we need rules (S17 or H17, DAS, LS, etc.)

Also, what happens to the streak bets on splits, doubles, insurance?

And, very importantly, the payouts for the 4 and 5 wins.

1) Dealer stands on all 17s.
2) Doubling on any two.
3) Aces split once.
4) Insurance offerred.
5) Streak bets can NOT be doubled. The money is in a separate ring above the main hand. After each and every hand, you have to re-bet the main hand and leave your Streak bets in the separate circles. It's a "side bet" on the number of consecutive hands, so to speak.
6) No DAS.

That do it?

1) What happens to the streak bet if you split and one hand wins while the other one loses? What if one pushes and the other wins or loses?

I see two ways to treat this, the first hand is only that counts or based net win or loss.

2) I do need to know payoffs for 4 and 5 wins.

Any push salvages the Streak bet, even if the second hand is a loss. A win does, too. Say you split eights, win one, lose one. Your Streak bet is STILL good, even though you lost one. Same if you push one and lose one. Lose both, streak bets go bye-bye.

That's another point. Let's say you bet 2,3,4, and 5 on the Streak circles. You are betting you will win 2, 3, 4, and 5 consecutive hands. If you lose on hand 3, the bets on 4 and 5 go bye bye.

Payout on 4: 16 to 1.

Payout on 5: 38 to 1.

If dealer shows an A and you take insurance, and dealer HAS it, Streak bets stay. If you don't take it and dealer has it, Streak bets are losses.

Just remembered. DAS IS permitted in Colorado games. And no surrender.

Using QFIT's numbers from http://www.bjstats.com/bjsc.asp, I get the following using HiLo.

 

Streak: 2 

TC   Prob.  Adv. 

 5  25.21% 0.85% 

 6  25.60% 2.38% 

 7  25.94% 3.78% 

 8  26.31% 5.26% 

 

Streak: 3 

TC   Prob.  Adv. 

 2  11.29%  1.60% 

 3  11.80%  6.22% 

 4  12.27% 10.41% 

 5  12.66% 13.94% 

 6  12.95% 16.54% 

 7  13.22% 18.94% 

 8  13.50% 21.49% 

 

Streak: 4 

TC   Prob.  Adv. 

 4   6.10%  3.62% 

 5   6.36%  8.07% 

 6   6.55% 11.37% 

 7   6.73% 14.43% 

 8   6.92% 17.71% 

 

Streak: 5 

TC   Prob.  Adv. 

 2   2.64%  2.84% 

 3   2.84% 10.75% 

 4   3.03% 18.12% 

 5   3.19% 24.49% 

 6   3.31% 29.26% 

 7   3.43% 33.71% 

 8   3.55% 38.53% 

 

Love the ten versus eleven thought.

OK, gonna try it soon. Let you know how I do.

Not doubling on 9, 10 vs 7-10, or soft double reduced the EV of your original bet by about 0.4%, but it does increase the probability of winning a hand by 0.11%. This does have a big effect on the results, particular the 5 streak. I don't have a calculation for the effect based on TC.

Also, once you've won a bet, do not take the bet down. It has more or less a 100% advantage at this point, even after a shuffle or the count going down.

Wouldn't the number of decks be important when considering the likelihood of streaks at different levels of the count? For example, if one were playing a single deck game, it is highly unlikely that he would get 5 rounds at a positive count, since you would have to discount the first round at least. I think one might be better off to simply look at the odds of winning X hands in a row and compare that to the odds being paid. If we use a winning percentage of 47.5% (we are discounting ties), then the odds would be as follows:

 

 

Streak             Odds         Odds paid          EV  

2                  3.43:1       3:1                -12.53%  

  

3                  8.33:1       8:1                -3.96%  

  

4                  18.64:1      16:1               -14.16%  

  

5                  40.35:1      38:1               -5.82% 

You're right in that there are end-deck conditions to be considered. Following is the thresholds at which the streak bets become positive based on the number of rounds left.

With 1 round left:

Streak 2: +14
Streak 3: +3
Streak 4: +14
Streak 5: +4

With 2 rounds left:

Streak 3: +2
Streak 4: +7
Streak 5: +3

With 3 rounds left:

Streak 4: +5
Streak 5: +2

With 4 rounds left:

Streak 5: +2

I believe the odds given for winning 4 bets is 18 to 1. Can somebody enlighten me about splits?wl (win-lose) counts as a push for the streak,wp is a win, wwl is a win ,llw is a loss, wlp is a push, lpp is a loss,wllp is a loss,etc.

I must have missed his description of the game in question.

Streak bet stays up and is neutral if you hit ANY push, no matter how many times you split. So, LLLP (splitting four times) is a push on the Streak bet.

Any win is a win on the Streak bet. LLLW would be a win on the Streak bet.

...let me know. I can let you know where the casinos are.

If you think it's beatable, and you want to take a swing, security's a joke here. I can actively TALK about counting with the dealers. Since the minimum and maximum bets are five bucks, they don't believe there's enough "higher math" to count the game.

And maybe, in a way, there isn't. What you'd have to do on sidecounts to calculate the Streak odds is pretty formidable -- MIT level, certainly.

But if you think you can do it, I'll jump in with you.