BlackJack Insurance Ė Is it a good bet?
by B.J. of Predictem.com
Several years ago, on my first visit to Las Vegas, I was playing BlackJack and I was dealt a 21 and the dealer flipped up an Ace for their card. The dealer asked if I wanted insurance, since this was my first time playing, I was confused. The dealer then explained that it was a no-brainer, I had a guaranteed winner so I obviously should take the even money payout. Is this the correct approach to take?
Letís examine and see if we can come up with an answer.
First of all, letís define what the bet is for those that may not be familiar with BlackJack insurance. In order to take the insurance you must bet Ĺ of your bet for insurance, if the bet wins, you are paid 2:1 odds. In the event that it wins then your original bet is a push. If the bet loses, then your original bet is a win that pays 3:2.
Letís look at an example:
Original bet - $10
If you get BlackJack and take insurance here are the possible results if you take insurance.
Dealer has BlackJack Ė Original bet pushes, insurance bet wins, net result +$10.
Dealer does not have BlackJack Ė Original bet wins $15, insurance bet loses $5, net result is +$10.
There are 4 possible scenarios that drive the decision on whether to take insurance.
1. You take insurance and the dealer has BlackJack Ė Win $10.
2. You take insurance and the dealer does not have BlackJack Ė Win $10.
3. You donít take insurance and the dealer has BlackJack - Push.
4. You donít take insurance and the dealer does not have BlackJack. Ė Win $15.
We need to assign a probability of each of the above scenarios. In a single deck game if you have BlackJack and the dealer has an Ace up you know that there 49 other possible cards that the dealer could have as a down card. Of those cards 15 are valued at 10 to give the dealer BlackJack and 34 will not allow the dealer to get BlackJack. Therefore, there is a 30.6% chance that the dealer will have BlackJack and a 69.4% chance that the dealer will not have BlackJack.
Of course no matter what happens if we take insurance our expected result is +$10. If we donít take insurance then we have a 69.4% chance of winning $15 and a 30.6% chance of a push. The expected result then would be $15 x 69.4% which is $10.41. This indicates that we are 4.1% better off by not taking insurance.
Of course this can change based on the composition of the remaining cards in the deck. If you are counting cards and you know that there are a lot of face cards left in the deck then it may be to your advantage to take the insurance.
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