Bets, bets and .. bets.

I ran all of the suggested responses with and without surrender except for the final one (bet 2/7 and double for less -- I'll handle that one separately).

BR1: bankroll 535, bet 40
BR2: bankroll 510, bet ???

Without Surrender:
BR2 response of 10 wins 47.68% of the time
BR2 response of 170 wins 48.23% of the time
BR2 response of 250 wins 48.37% of the time
BR2 response of 350 wins 48.21% of the time

The big bet responses differ only slightly due to minor differences in split/double coverage.

With Surrender
BR2 response of 10 wins 43.77% of the time
BR2 response of 170 wins 44.07% of the time
BR2 response of 250 wins 44.06% of the time
BR2 response of 350 wins 43.27% of the time

Since all of these responses can beat BR1's surrender, it becomes a matter if winning the hand for BR2, should BR1 do so. BR1's optimal strategy here is to surrender most hands in order to force BR2 to do just that. Minor differences here are also due to split/double coverage.

 

Regarding the suggested response of 145 (2/7 of total bankroll) combined with the possibility of doubling for less on the first hand of a split and then playing the second hand accordingly, I analysed this one a couple of years ago for S. Yama. When I first introduced the existence of my simulator to this forum, he wrote to me privately and asked me to analyse it, calling it "The Masonuc Manoeuvre".

I generated the optimal strategy for betting 2/7 of one's total bankroll with the goal of winning 1/7 or more and with double for 50% available. The resulting strategy was then simulated to find out the success rate. I then also compared this to betting one chip more than 2/7 (making the manoeuvre impossible) and to simply betting 1/7, both with the same goal of winning 1/7 or more.

The results were that the manoeuvre has very little benefit:

1. Bet 2/7: 43.85%
2. Bet 2/7 + a chip: 43.75%
3. Bet 1/7: 43.78%

This may be because the situation does not arise frequently enough to have a significant impact. Note that the strategy for the first two cards for the manoeuvre (1 above) is the same as recommended for winning 1 bet without double for less (3 above) (including the recommended splits):

http://gronbog.org/results/blackjac...one/generated/complete/1.0/p1.X/strategy.html

So the benefit of the manoeuvre can be quantified as 0.07%