 In the case of heads, you receive $2.00 and for tails you get nothing. You will no doubt be happy to play this game as it has an expected monetary value (EMV) of $1.00. How much would you be willing sell your ticket for? It is unlikely anyone will pay you much more than $1.00 and if you sell it for much less you are “giving away” EMV. Now consider another game. In this game you have to buy a ticket. In this game a heads pays $3.00 and a tail pays $1.00. How much would you be willing to pay for this ticket? The EMV of this game is $2.00 and if you pay any less than that you are (on an expected value basis) gaining money. Would you pay more than $1.00? If you paid $1.00, the second game becomes equivalent to the first with the net result of a head being $3.00 – $1.00 = $2.00 and the result of a tail would be $1 -$1 = 0. Is there a difference in how much you are willing to sell your ticket for in the first game and what you are willing to pay for it in the second game? Decision makers often make decisions on other than an expected value basis based on how much investment exposure is necessary.
Let’s consider another set of decisions. In the first option, you pay €1,000 by investing in a very small percentage (0.1%) of a drilling well that you anticipate has a 50% chance of success (or a coin flip for heads if you prefer). In the case of a discovery you win a series of cash flows with an NPV of €4,000 while a dry hole pays nothing. The EMV is 0.5*€4,000 – €1,000 = €1,000. Are you interested in this investment? If you believe these numbers and have 1,000 euros (€) to invest it is an obvious decision to participate in the project. Now let’s look at the 100% working interest position. In this case you need to invest €1,000,000 and have a 50% chance of €4,000,000. Assume that your net worth is just enough that you could come up with the money by mortgaging your house, cashing in your retirement and borrowing all of the money that you can; it is unlikely that you would accept such an investment opportunity. A single investment or a series of investments that have the potential to bankrupt an investor is known as “gambler’s ruin.” Your utility for a positive €1,000,000 is considerably less than 1,000 times greater than it is for €1,000. By analyzing your responses to a series of similarly constructed alternatives, an individual with game theory expertise could construct your “indifference curve.” Your personal utility and indifference curves and those of the decision maker are not as important as is the utility functions of the corporation. For our purposes we will assume that the corporation has a unit slope linear utility function and makes its decisions entirely on EMV. Exceptions to this would only occur for massive investments.
In the drill vs farmout example, we had a decision tree that looked like the following:
There were only two decisions, drill or farmout. The probability nodes were only dry hole or discovery. The analysis of a decision tree proceeds from right to left as the EMV is calculated for each probability node. The expected value of each probability node is replaced with its expected value and the highest EMV decision node is selected. There can be multiple probabilities at each probability and the probability node can be replaced by Monte Carlo simulations. In fact, the entire decision tree can be replaced by Monte Carlo simulations with a distribution of decisions being made and the corresponding variability in results conveyed to decision makers.
 Consider the trivial case of 38 players each betting $1,000 on one each of the 38 spots and play one time. One person will walk away with $36,000 (his bet plus his $35,000 in winnings) while 37 players lose their bets. The house makes $2,000.
 Coin collectors refer to the obverse and reverse of a coin rather than “heads” or “tails” but we will use the more common convention.