QUESTION: Suppose someone offers you the following gamble: You pay $7 and toss a

Question

QUESTION: Suppose someone offers you the following gamble: You pay $7 and toss a coin. If the coin comes up heads, he pays you $10, and if tails comes up, he pays you $5. You in turn get the idea of offering another person a coin toss in which he pays you $7 and tosses another coin. You tell him that if heads comes up, you will pay him $9, and if tails comes up, you will pay him $5. You think you see an opportunity to earn an arbitrage profit by engaging in both transactions at the same time. Why is this not an arbitrage opportunity? How could you make it one assuming that you could get two people to engage in these gambles?

ANSWER: Arbitrage is buying low and selling high in order to make a profit. The coin toss is not considered an arbitrage opportunity because you may incur a loss just as easily as you may realize a profit. By entering into the toss as described you cover the $7 cost of the toss, but may end up breaking even, with a net loss, or with a net profit. The four scenarios with the two bets are possible:  

Scenario          Flip                Net Profit / (Loss)

        1         Heads, Heads                  $1

        2          Tails, Tails                        $0

        3          Heads, Tails                     $5

        4          Tails, Heads                    ($4)

Assuming you can get two people to engage in a coin toss, you can make it an arbitrage opportunity by ensuring each outcome results in a net profit. However, it seems unlikely that this will happen as the prices will begin to converge at some point and eliminate the opportunity for arbitrage. For example, in order to make a profit in all four scenarios both payouts in the second bet would need to be less than $5 or the cost of the bet would need to be higher to cover the potential losses. It is unlikely that an individual would pay money to enter a bet that has zero chance of covering the cost. I believe that this is the law of one price, which states that two identical outcomes cannot sell for different prices.

PLEASE COMMENT ON MY ANSWER.

Explanation / Answer

Yes, your analysis to the situation is correct, the outcome is purely depending upon the probability, the certainty of outcomes is not in your hand hence there is not an opportunity of arbitration however, if You can reduce the paying amount below $5 in both the cases in second bet, this will definately going to give you an opportunity of arbitration but getting a person who will choose this betting offer is highly impossible, since the person wont be any profit invloved in this transaction.

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