# Player insurance on natural player blackjack

Assuming that the dealer has a ACE as their up-card. Then normally, the player is asked to take insurance.

If the player has natural blackjack, can he still take insurance?

If the bet value is \$1 and if the player takes insurance and dealer has blackjack, what is the player win? Is it EVEN MONEY + BET/2 (insurance pay) = \$2, after paying \$1(initial bet) + \$0.50(insurance)

• Having a face-card up is mutually exclusive with having an ace up. Please fix your terminology to make sense. – Nij Mar 16 '17 at 3:29
• @Nij Actually for the matter of the insurance bet, it only happens when the dealer has an Ace as the face up card. You don't see the dealer's second card until the players have finished playing their hands. – LeppyR64 Mar 17 '17 at 11:59
• I think I know how blackjack works, it was my job for years. Aces are not face-cards, so it is impossible to have both a face-card and an ace exposed. – Nij Mar 17 '17 at 19:19

# Assuming the Player Has Blackjack

If you take the insurance:
If the dealer has Blackjack you will earn \$1.00 on the hand.
If the dealer does not have Blackjack you will earn \$1.00. (\$1.50 - \$0.50)

If you don't take the insurance:
If the dealer has Blackjack you will earn \$0.00.
If the dealer does not have Blackjack you will earn \$1.50.

Ultimately you won't lose money taking the insurance bet, but you will lessen your earnings. It will all depend on the odds of the dealer having Blackjack.

The odds of the dealer having Blackjack where this choice has the same expected value is 1/3. If there's less than 1/3 chance of dealer having Blackjack, you should not take Insurance. If there is greater than 1/3 chance then you should take insurance.

On an initial deck/shoe/whatever, there is about a 30% chance of dealer having Blackjack.

# Assuming the Player Does Not Have Blackjack

If the dealer has Blackjack then the player will break even. (\$1.00 win from Insurance - \$1.00 original bet)

If the dealer does not have Blackjack then the earnings will be the earnings from the hand less the insurance bet. (Earn \$0.50 if the hand wins, Lose \$1.50 if the hand loses)

• You are assuming that the natural blackjack pays bet*3 (payout is 2:1), correct? – NVG Mar 15 '17 at 14:44
• Math is hard sometimes... Blackjack is usually 3:2. I will correct. – LeppyR64 Mar 15 '17 at 14:45
• Yes, blackjack is usually 3:2, so the win is bet*2.5. – NVG Mar 15 '17 at 14:46
• @NVG No the win is still only \$1.50, but you don't lose your bet. – LeppyR64 Mar 15 '17 at 14:48
• Win is not the same thing with profit. Win is what the game pays at the end. If I bet 1\$ and I have blackjack, the win is 2.5\$, while the profit is 1.5\$. If I bet 1\$ and I have no blackjack and I take insurance, then I pay a total of 1.5\$ (bet+insurance_bet). Then if the dealer has blackjack, I win 1.5\$ or 1\$? This is my dilema. – NVG Mar 15 '17 at 14:55

If the player has a natural 21 (a "blackjack"), the insurance offer is instead called "taking even money." The dealer will offer to pay the hand at 1:1 before revealing the hole card. If the player accepts this offer, they get paid immediately. If the player refuses "even money," the dealer then checks: a player win is paid at 3:2; a player push — both parties have 21 — means no money is won or lost.

Mathematically, this is equivalent to taking insurance because it the half-bet that would normally be staked as insurance is the same half-bet that is forfeited with the 1:1 payout.