Ken, I know you are *not* totally convinced
that your expected return does NOT change by setting stop-loss/stop-win limits.
Many people already stated that "it's just one lifelong session", and that's a very good way to look at this issue. Here lemme just try and point out the fallacy in your argument in one of your previous emails:
>> These are just some random numbers, but say somehow your ROR for each day was 5% with 10 units (to make one unit). Out of 100 days, you would lose 10 units on 5 of those days (-50 units). And on 95 of those days you would win just over 1 unit each day (with bj's or double downs, etc.), about +100 units. So after 100 days youd average up about 50 units.
Let's suppose your edge against the house is 0% so that your long term expected return (that is, if you played *continuously* without arbitrary stop limits) is zero. (You can use positive EV, but it does not change the logic explained here.) Now let's divide your lifelong session into multiple small mini-sessions with fixed stop-win and stop-loss limits.
[A] Stop-win: $100, Stop-loss: $100
You will end up a winner 50% of the mini-sessions and you will quit as a loser 50% of the times.
--> Your expected return = 0.5 * 100 + 0.5 * (-100) = $0
[B] Stop-win: $10, Stop-loss: $100
You will be a winner 10 out of 11 mini-sessions and you will quit as a loser 1 out of 11 times.
--> Your expected return = (10/11) * 10 + (1/11) * (-100) = $0
[C] Stop-win: $1, Stop-loss: $100
You will be a winner 100 out of 101 mini-sessions and you will quit as a loser 1 out of 101 times.
--> Your expected return = (100/101) * 1 + (1/101) * (-100) = $0
Note that you will win far more frequently, but your occasional losses will totaly wipe out your cumulative wins. (Counter-example to your argument.)
[D] Ad infinitum....
Again, adding any positive EV in your setup does NOT change this argument. [[Your expected gain from a long (continuous or not) session without stop limits are EXACTLY the same as the one from many small mini-sessions with stop-win/stop-loss limits (whatever those limits are).]]
I hope my argument is clear enough to renounce the idea of "using stop limits to gain EV". Having said that, setting stop limits are *extremely* important in my opinion. I am not going go into details here, but most recreational gamblers end up losers not because they don't know how to play blackjack but because they don't understand this concept behind stop limits (usually set implicitly by the amount of their "pocket money").
~Black Jack in the Box.