Probability Question

Hello all,

Tonight, when using an online playing card simulator that deals cards out from a specified number of decks, I dealt myself hands to examine my non-counting, non-progression/regression, non-Voodoo strategy. In 40 hands, I was ahead 5 units, which I know is virtually meaningless.

But, beginning with Hand #10, I experienced a 9.5 unit win streak within the span of 10 hands. Specifically, I had win, win, win, win, push, win, win, win, BJ, win. (Note: I cannot simply consult a chart displaying the probabilities of consecutive wins because I had a 'push' in the middle of the string of wins.).

Can someone please tell me the likelihood of this happening with flat betting, Double Deck, Dealer hits soft 17, no Surrender, doubling after splitting allowed, Player gets 1 card for each Ace after the player splits Aces, "average" penetration, BJ pays 3:2, Dealer is right-handed and wears glasses :)? I'm thinking this has got to be in the ballpark of 1 in 90,000 or so.

I realize many of us have anecdotal evidence of such rare events ("Hell, just last night I won 76 hands in a row and then single-handedly wrestled two casino thieves to the ground..."). No offense meant, but I am really interested in the cold, hard math please.

On average, you win a BJ hand about 43% of the time, lose 48%, and push 9%. You get a untied blackjack in DD about 4.59% of the time.

So, getting 8 wins, one push, and one natural in exactly that order happens (0.43)^8 * (0.09) * (0.046) of the time, or 0.000484% of the time, or once in 206,658 tries.

But the above has to be multiplied by C10,2, to allow for the fact the the natural and the push could occur anywhere in the sequence of 10. C10,2 = 45, so the final probability is 1 in 4,592.

Don

Yes, that's right. Usually, with these types of problems, there are only two possible outcomes, not three. So, if it were, say, 8 wins and 2 losses, we would multiply by C10,2. But, since the push and the natural are different results, we need P10,2, that is, we need permutations and not combinations, because the order matters.

Thanks for pointing this out.

Don

++
Learn a lot here. Sometimes when Mr Schlesinger comments; It goes over my head. The math is intent sometimes, take note of previous word.

I respect those lesser or moorer than myself, knowing we all have something special. Of course there are exceptions.

I've learned thru Don. My math skills & spelling less.

It is kind of like reading. Sometimes while reading, I will come across a word I don't understand. note, this is how you real AP's teach me.

It takes a long time as well as thought pattern to stop. Many times I will continue without word check etc. Odds are that reading on will cause you to all a sudden understand that word.

Thru time. Even the most complicated becomes simple. There are many endeavors in life that we start weak and latter become very strong.

And we get it; With a little help from are friends. Or maybe a whole lot from our friends.

Good Cards,,,, LWC

Thank you both for your responses. But I cannot help but feel something is amiss. I do not care about the order or even what contributed to the 9.5 units. I am just interested to know what the probability of plucking a set of 10 consecutive decisions that total 9.5 units from the results of a computer simulation printout is.