Insurance with card counting

"On average, when the dealer has an ace up, the remaining cards in blackjack will be 30.87% tens (based on a six-deck game), making insurance a bad bet. However, if the probability gets above 33.33%, it becomes a good bet."

I don't really understand why above 33.33%. Since insurance pays 2:1, from 100 times the player wins 33.3 times (33.33 plus), and lose 66.66. So the player lost 33$ in total, didn't?

Why it isn't a good bet above 50%?

Thank you!

So, one third of the time you win $200
Two-thirds of the time you lose $100

$200 * 1/3 is equal to $100 * 2/3
that is a net break even

When the probability of winning is above 1/3, the probability of losing is less than 2/3, so
$200 * > 1/3 is greater than $100 * < 2/3
that is a net gain

Quote: tusker

"On average, when the dealer has an ace up, the remaining cards in blackjack will be 30.87% tens (based on a six-deck game), making insurance a bad bet. However, if the probability gets above 33.33%, it becomes a good bet."

I don't really understand why above 33.33%. Since insurance pays 2:1, from 100 times the player wins 33.3 times (33.33 plus), and lose 66.66. So the player lost 33$ in total, didn't?

Why it isn't a good bet above 50%?

Thank you!

Insurance pays 2 to 1. The 33.3333 times the payer wins he wins 66.6666 The 66.6666 times he loses he loses 66.6666.

To convert from ratio to percentage form convert to 1 in form (so 1:2 becomes 1 in 3) then divide 100 by the bottom number. So 100 divided by 3 = 33.33%

From 100 times the player wins 33.3 times, paying 66.6 units profit (pays 2 for every 1 u bet). He also loses 66.6 times, losing 1 unit. So he breaks even.



pro tip : with a strong hand like 20, or even 21 in jusisdictions that play without a hole card but allow you to take insurance after you resolve your hand, insure slightly below the index