math and probability geniuses... i need help

here's the probability question:

lets say you place a trade which has a 50/50 chance of being favorable. if it is unfavorable you lose $100. if it is favorable, you have 60% chance of making $100, 20% chance of making $240, and a 20% chance of losing $30 (commissions).

should you place the trade, and what is your probability of each level of profit or loss? since there are four possible outcomes, what are the chances of each?

thanks in advance.

 

30% x 100 = 30
10% x 240 = 24
10% x (30) = (3)

50% x (100) = (50)

Total = 1

 

Expectation = (prob. of win * size of win) - (prob. of loss * size of loss)

In this case the size of win is a distribution:

.6*100 = 60
.2* 240 = 48
.2* -30 = -6

The size of win is 60+48-6 = 102

Solving for expectancy:

E = (.5*102) - (.5*-100)
E = 51 - 50
E = 1

I wouldn't waste my time trading this low of an expectation, but a scalper might love it.

 

I'll take it. Enlighten us, what is the trade?

 

Your scenario is ambiguous.
You include "20% chance of losing $30 (commissions)" as one of the "favorable" cases. One might *assume* that you mean "20% chance of a break-even [you call that "favorable"?] with $30 lost to commissions."

Please be more explicit. Is a $30 commission already factored into the other cases?

 

Yeah really, for a guy like me who doesn't know how to program systems, I would buy a book of just easy to follow systems that should break even.

 

That's better than one of the alternatives.

 

alright, i should've just asked my original question. however, it has nothing to do with trading, so i changed my question to suit this forum.

to understand the question, you need to have a decent knowledge of betting sports.

basically, i have a place that will offer a certain bet that i have not seen offered before. they will allow me to parlay the first half of a basketball or football game to the money line on the same team to win the game. since you have roughly a 50/50 chance of winning the first half bet, the chances of winning the second half of your parlay is significantly higher if it's a team that already has a lead.

i.e., last night i parlayed the first half of gb to gb to win the game. a $20 bet to pay $34.

the reason i posted the original question was to find out if i had an edge over this sports book. immediately after i posted my question, i realized the math was simple. i was just being lazy.

i realize that without any data, it is impossible to figure out if i have an edge.

 

nothing is impossible.

and its also improbable

 

expected return on win = $57
expected loss = $50

I think