How often can we expect to get Blackjack?
Blackjack is game to get 21, but what are the chances to get 21? When a player gets an Ace and face card and the dealer doesn’t have 21, the player would have a Blackjack and receives 1:5 times his bet for that hand, or 1.5:1 Blackjack payout. In another words if player bets 10$ and scores a Blackjack, the player would receive 15$ from the dealer. What’s the probability of getting that Blackjack?
What’s the probability of getting that Blackjack?
Well you start to think how many aces and face cards are left I hope. With one deck there are four aces out of 52 cards, and 16 face cards. Once you account for the aces you know one ace would be out of the picture yielding
The Expected Value is the average value, or the average number of expected Blackjack’s to occur.
If you play 100 hands of Blackjack in one night, you are expected to get Blackjack only 4 or 5 times. Without considering a betting strategy that’s no Blackjacks 94 and 95 times out of the 100. The average Expected Value is not an accurate number you can depend on anyway… So let’s bring in a 95% confidence interval to test variability of occurrence. Using the standard deviation, which comes from calculating the variance, we can measure variability of the Blackjack’s.
The values of 0.87 and 8.79 are hard to picture, so we can round to the closest whole number. The 0.87 will be rounded down, because it’s the lower limit to 0. And, the 8.79 value is rounded up, because it’s the upper limit to the value of 9. In conclusion, we can be about 95% certain we will get Blackjack between 0 and 9 times out of 100 hands.
