View Full Version : Blackjack probability question

09-07-2005, 04:34 PM
I was casino whoring some blackjack, and running bad. I noticed that I seemed to lose an inordinate number of my double down bets, so I decided to start tracking them to see how many I would win. Over the course of around 800 hands playing perfect basic strategy, I ended up winning 7 times, and losing 17 – for an overall winning percentage of 29%.

Obviously various double down situations have a greater chance of winning than others (doubling your eleven vs. a six clearly is more advantageous than doubling against a nine), but obviously all double down situations have to have a greater than 50% chance of winning or you wouldn’t be advised to double.

Despite this small sample size, I wondered if anyone knew a way to calculate the probabilities of a losing streak in this range, assuming an expected winning percentage of a double down hand to be around 51-52% (I tried to do a search to find what the average expected win percentage of all doubling hands combined were, but couldn’t find it).

I’m mostly just trying to gauge how bad I am running, and if there is a possibility of the casino skewing the deck.

09-07-2005, 04:43 PM
For sake of argument and conservativism, say your probability of winning is only 51% on your double downs (it's not, but for sake of argument).

The odds of you winning 7 or less times out of 24 are:

=BINOMDIST(7,24,.51,TRUE) or about 2.55%

You're running pretty bad, but the sample size is really small, regardless. I haven't analyzed blackjack that thoroughly, but if your odds are 60% on each, it's obvious worse at .22%.