Hopefully someone can clarify for me what I am confused about.
I created a spreadsheet first with all combinations of 4 hands with each hand possibly being a win or a loss, no pushes, doubles, splits, or BJ's, for a total of 16 different scenarios.
Then I simulated a simple progression I use for each of those scenarios, and as expected, the sum of all scenarios summed up equalled 0. No suprises here based on the 50/50 thing I was simulating.
The next step is what caused me great confusion. I wanted to compare this approach to flat betting, but I made my flat bet for each scenario equal to the average of the 4 bets I would have played over the course of those 4 bets. Meaning, for each scenario, the average flat bet could be different. I took the 4 progression bets, added them up, and divided by 4 to get my flat bet.
I know that if I entered the same flat bet for each bet for every scenario, my sum would be equal to 0. The problem is using my average for the 4 bets as the flat bet for each scenario resulted in a total of -$120 total for the sum of all 16 scenarios. (My base unit used in the progression was $10, and I would increase by $10 on a loss, decrease by $10 on a win, and stay at $10 on consecutive wins if already at that level).
Can anyone explain to me what is going on here? I have verified my calculations and formulas 3 times and can not come up with anything. Maybe someone can duplicate the above scenario, or someone already knows the answer. I apologize to those I need to, but the progressions I have played have worked and continue to work for me year after year. I know this does not duplicate real BJ play, but I expected the sum of all bets to be 0 for both situations, and need help thinking about this.
If I made a mathematical error that I did not catch, I apologize for that also. I will probably find it the moment I hit the "Post Message" button.
Dave
