Hello! I am trying to figure out the math of this problem step by step. Can someone spell out how they arrived at the below profits?
suppose someone places a $100 bet on X at odds of 10 to 1 against X, and later he is able to place a $600 bet against X at odds of 1 to 1 against X. Whatever the outcome of X, that person makes a riskless profit (equal to $400 if X occurs and $500 if X does not occur) because the implied probabilities are inconsistent.
Suppose that X occurs. He wins the first bet, but loses the second. The net result is $1,000 (first bet) − $600 (second bet) = $400.
Suppose that X fails to occur. He loses the first bet, but wins the second. The net result is −$100 (first bet) + $600 (second bet) = $500.
Sorry still not understanding - perhaps it’s the wording
1st bet: he’s betting that X will or won’t happen?
2nd bet: he’s betting that X will or won’t happen?
Also, I’m confused how you get the dollar amounts using the probabilities stated as odds equations. trouble you to break that out?
My mistake: I wrote the outcomes backwards. Sorry. I’ve corrected them.
In the first bet, he’s betting that X will occur.
In the second bet, he’s betting that X won’t occur.
If you bet $1 at odds of Y:1, then if you lose, you lose $1 (your bet), and if you win, you win $Y.
In the first bet, he’s betting $100 at 10:1. If he loses, he loses $100 (his bet); if he wins, he wins 10 × $100 = $1,000.
In the second bet, he’s betting $600 at 1:1. If he loses, he loses $600 (his bet); if he wins, he wins 1 × $600 = $600.
No problem - thank you for your help!
My pleasure.