The Coin-Tossing Methodology

From Stanford Wong's BJ21

Posted by MathProf on 25 Aug 1998, 5:08 am, in response to Effect of Trip Ruin on Trip EV (A longy but a goody), posted by MathProf on 25 Aug 1998, 4:54 am

I have used a coin tossing model for the study above. I view the trip as a series of coin tosses, and then calculate, after each toss, the exact probability distribution. This is very to do ( I store the probabilities in an array.) When done, I have the complete distribution of player results. I used this distribution to compute the Trip Statistics that were posted.

As I have set up the program, a StopWin must be set. Originally, my purpose in doing this was to study the effects of such a Stop Win. However, it simplifies the programming a bit, because I use a fixe length array. And as I said, you can put in a very large number to make the SW effectively infinite.

How many coin tosses go into a trip? For the runs that were posted, I used 10,000 coin tosses. However I experimented with some other values for a few representative cases. I look at 40,000 tosses and 100 tosses. The results did not vary noticeably for these different values. (In all cases, the coin tossing parameters are chosen so that the total EV, SD, StopLoss and StopWin are identical with the Trip.)

I have spot checked the RoR computed against Don's formula and they agree in the second, and usually the third decimal place. For the examples I looked at.