Expert: Scotto - 6/23/2009

Question
QUESTION: There are four independant systems that generate either a Win or Loss output.The Win % on each system per month is  28%,35%,45% & 62%. What is my overall winning % each month?TH? .

ANSWER: THe win on the total of four systems, assuming they are all independent of each other and played separately, is found by adding up the probabilities.  That will give you the number of wins you get each month at four games of gambling.

That would be 0.28 + 0.35 + 0.45 + 0.62 = 1.70.

That means out of of four games, you could almost expect to win two.
If this were done for ten months, the average says that 17 of the games would have been won out of the 40 played.


I don't know what TH? means.

Is that for these odds being Tail/Head
on four different biased coins?


The chance of winning all of the probabilitities would be
the product of 0.28, 0.35, 0.45, and 0.62.

That would be 0.027342.

The chance of winning all but one would be the sum of four sets of four probabilities where three were one and the other lossed.  The chance of losing each one is one minus the chance of winning.

These would be 1 - 0.28= 0.72; 1 - 0.35 = 0.65;
1 - 0.45= 0.55; and 1 - 0.62 = 0.38.
The chane of getting at only three wins would be the sum
0.016758 + 0.033418 + 0.050778 + 0.070308 = 0.171262.

The chance of getting at only 2 wins would be the sum of 6 products.
You could win 1&2, 1&3, 1&4, 2&3, 2&4, or 3&4.  The final answer is
0.373262.

I put the chances in a spreadsheet and calculated the odds of winning 0, 1, 2, 3 or 4 games.
For 0 games, the chance is 0.097812.
For 1 game, the chance is 0.330322.
For 2 games, the chance is 0.373262.
For 3 games, the chance is 0.171262.
For 4 games, the chance is 0.027342.

So even though two games is the most likely, the arerage is less than 2 since the chance of winning less than two is 0.428134 and the chance of winning more than two is only 0.198604.

Does this have anything at all to do with TH?



---------- FOLLOW-UP ----------

QUESTION: Hi,
Many thanks for your time & prompt response.
Forget TH this should have been deleted.Apolodies for any confusion caused. From the first part of your answer where you take the figures over ten months does this mean that my chances of winning each month are 17/40=0.425=42.5% I am looking at this from a trading perspective.If each system generated 100 trades/month with the same percentages as per original question how many winning trades would I have each month?
Also would appreciate copy of your spreadsheet where I could plug in the number of trades for each system, the winning percentages & the individual & overall outputs. My e-mail is
Many thanks for your time.
Best regards
Russell

Answer
On the average you would get a little less than 43 wins per month.

Unless they have more of an even payoff, I see them as being a waste of time.  However, I'm sure they probably are paying more than what is invested, of course.

I'd love to mail to your e-mail address.  

Well, Russell, I'd be glad to mail it,
but I think if I mailed it to ________@____ { a blank address },
it wouldn't get there.

What's you e-mail addresss again?  It didn't show up in this message.