justme said:
The bottom line....I really need to run sim and see what happens
yaddayadda....
You should get a pencil.
Step 1. Formulate your betting system so that there is no question about what to bet at any time.
Step 2. Write all combinations of wins and losses of, say, 5 hands in a list. Ignore pushes and doubles/splits. Hint: those are 2^5 = 32 possible sequences.
Step 3. Apply your betting system to each of those sequences. Be very strict in following your betting system (as on the paper you know your future wins/losses, when betting in a real game you don't know). Note down the total win or loss in that sequence.
Step 4. Calculate the probability of each sequence. If you have 5 hands, multiply 0.505 for each each loss occuring, and 0.495 for each win occuring in that sequence with at least . For the sequence WWLWL it would be 0.495*0.495*0.505*0.495*0.505 = 0.030931313
Step 5. Add up all probabilities. How close do you get to 1.000000000 ?
Step 6. For each sequence, multiply the probability with the win/loss, call that the expected win/loss.
Step 7. Add up all expected wins/losses, and divide by the number you got in Step 5.
I bet my house (and my wife:laugh
that (if steps followed correctly) your resulting number will be NEGATIVE.