Alan, I added a variable to my program that keeps track of the maximum wins in a row. I ran the program for 10,000 sessions playing BP with win/loss goals of 250/2500 ... and the maximum wins in a row came out to 31. However, the overall return was still right at 99.1%.

So, the good news is you could win a lot more of your sessions before that first loss. The bad news is it won't make much difference in your overall results over time.