Sometimes you do, sometimes you don't
Another thought provoking scenario and questions by PlayHunter.
Though, as a very general rule, one should take insurance if dealer’s blackjack gives him advancement, particular cards, bets and bankrolls play important role.
PlayHunter asks about players’ strong hands 18 to 20 vs. dealer’s Ace and the specific already done bankrolls and bets. That is nine different plays and chances, and when soft hands are included there will be 36 situations to consider!
BR1: bankroll 2701, bet 800; BR2: bankroll 2300, bet 1000, dealer shows an Ace.
We are assuming, as gronbog wrote, that that if BR1 takes insurance, then BR2 does not, and that if BR1 does not take insurance, then BR2 does.
The first decision BR1 has to make is to whether take insurance or not. Then, assuming there is no dealer’s blackjack the options are to surrender, stand, or double. The double for BR1 should be for less (200), as after losing the insurance bet he has one (1) chip more than BR2, and having bet of 800 vs. the opponent 1000 – it does all that’s needed.
Lets look at what happens when BR1 and BR2 both have hard 18.
(All numbers are for BR2 chances, though we consider BR1 insurance)
The optimal play for BR1 is to take insurance and then surrender for total BR2 chances of success 37.7%.
If BR1 loses insurance and stands on his 18, then BR2 can surrender for his 31.6% chance.
If BR1 doesn’t take insurance he can stand and BR2 can not surrender, so he has to double for his total chances of winning 45%. BR1 surrendering offers BR2 (stand) chance of 55%.
BR1 18 and BR2 19.
The optimal play for BR1 is to not take insurance and stand, BR2 standing achieves success 44% of the times, BR2 doubling brings it down to 39.5%.
When BR1 takes insurance and then either stand or surrender, best play for BR2 is to stand and it advances him when the dealer has bust to 19, for total BR2 chances of success 50.8%
There is an interesting play by BR1: after unsuccessful insurance he can double down for 200. If BR2 plays optimally and sees BR1 doubled card he wins the match almost 57% of the time.
However, if the doubled card is not shown and BR2 makes mistake of doubling too, he reduces his chances to 10%. That means that if BR1’s opponent makes this mistake once in four plays then the expected outcome is better than the optimal play of not taking insurance.
BR1 18 and BR2 20.
Here, the optimal play for BR1 is to not take insurance and stand, BR2 standing achieves success 57.1% of the times, BR2 splitting brings it down to 52.6%.
A close second play is to take insurance and then double for 200, where BR2 surrenders if BR1 busts but splits his Tens if BR1 improves, for BR2 total chances of about 58.5%.
BR1 taking insurance and then surrendering gives BR2 64.1% chance to win the match.
S. Yama
