I spend a lot of time around will contests. I represent people challenging wills and people who are defending wills against challenges. I mediate and facilitate settlement of will contest cases filed by other lawyers. I write wills that I know will be contested, and thereafter testify in court about what I did. I think a lot about will contests. In this post I want talk math of will contests.

In almost every probate someone files a will and claims that the will accurately states the wishes of the decedent (the dead person) about how his or her property should be distributed. In a will contest, a challenger alleges either that the decedent died without a will or that the estate should be distributed according to the terms of an earlier will because the will admitted to probate is void. (For more on legal strategies for challenging a will in Oregon, click here.) If the decedent died intestate--that is, without a will--the State of Oregon has written one for him. A will contest always pits one proposed distribution against another.

Ordinarily, the proponent of each will is the person who will benefit most from it. If Adam is the decedent. Cain will advocate for the will that leaves everything to Cain, and Abel will advocate for the will that leaves everything to Abel. In will contests there is no way for a court to split the baby. Either Cain wins or Able wins. For this reason, will contests are a zero sum games.

Because there are only two possible outcomes--like flipping a coin--will contests lend themselves to a mathematical computation of value. If there were a hundred dollars on a table you got to flip a coin with another person to see who gets the money, you would have a 50% chance of winning the money. The opportunity to flip for the hundred dollars is worth .5 x $100, or $50. If you got to play the game a hundred times, you would win about half of the flips. If you won fifty flips out of a hundred you would take home $5,000, or $50 per flip. In the world of probabilities this is called expected value. If you only got to play once, but were not a risk taker you might agree with the other flipper not to flip at all and simply split the money. You and the other person each would take the expected value of the opportunity and walk away with fifty dollars.

No one would do a will contest for a hundred dollars, but a person might do one if there were $500,000 on the table. If Adam had died with a nice home and/or a good sized investment account, there might be this amount for Cain and Abel to argue about. Personal injury lawyers wait around hoping for a case in which there is $500,000 to divide. Probate lawyers get these cases all the time.

When you flip a coin, you know the odds of it coming up heads or tails. It is 50/50. In a will contest, however, the odds of winning are unknown. Let's assume that Abel got to the courthouse first and it is Cain that is challenging the will that favors Abel. If the odds of Abel winning are the same as flipping a coin--50/50--then the opportunity to play is worth $250,000. That is the expected value. It is also the default settlement value of the case.

Will contests, unlike coin flips, do not lend themselves to a simple calculation of the odds of winning. Emotions run high, with both sides willing to go to court because both loved Adam more than anyone else in the world and both believe they represent what Adam really wanted. If you can set emotions aside, however, the case can be evaluated in terms of chances of success in the same way as we did with the coin and the $100. Let's say that Cain's case is weak, and everyone who looks at the cases agrees that he only has a two in ten chance of winning. The math is the same as the coin flip with different numbers: .2 x $500,000 = $100,000. Cain's case is worth $100,000, and in an emotionless world, Abel would settle by taking $400,000 and giving Cain $100,000. Both Cain and Abel, like our coin flippers, walk away with the expected value of their respective cases.

(It is important here to avoid the kinds of errors that plague gamblers and politicians. First, Abel may say, "I have an 80% chance of winning this case and taking all the money. Why should I give Cain anything?" This reasoning conflates a high likelihood of something happening with certainty. The 80% chance of winning means that if you tried this case ten times before ten different judges, Abel would lose two of the cases. In real life, Abel only gets to try the case once and that once could be one of the one that loses.)

Unlike my example with the coin flip, a will contest is not free. It is like a lottery in that there is a cost to play. The cost of a will contest is the litigation costs--both attorney fees and court costs--and those costs need to be deducted from the value of the case in the same way that the costs of a lottery ticket reduce its expected value (The expected value of a lottery ticket is always less than you paid for it). So lets say that it costs $50,000 to litigate a will contest. If Cain settles his case on an expected value of $100,000, he would owe his lawyer $50,000 (or less if he settles early) and walk away with $50,000 in his pocket.

But wait a minute, Cain knows early on that he has an 80% chance of losing his case. Thus it is quite likely that he will have to go to court, lose the case, get nothing, and end up owing his lawyer $50,000. When you don't win the lottery, you are still out the cost of the ticket. Thus, Cain faces a situation in which he must pay $50,000 for a .2 probability of receiving $500,000. Avoiding the $50,000 debt may be more important to him than the small chance of a large payoff. If Cain is wealthy and mathematically inclined he will pursue the .2 chance of getting $500,000 every time. If Cain is very poor and has no intention of paying his lawyer unless he wins he will similarly take it every time. If Cain, however, is an average guy who takes his debts seriously he may forgo both the case and the cost. The payoff may be mathematically justifiable but the risk of loss is too great.

Abel has it better. He only has a two in ten chance of getting nothing and ending up with a big bill for attorney fees. If he has a lot of money and is mathematically inclined, he will try or settle the case indifferent to the outcome because he knows that over the long run it was a wise investment. The middle class Abel will defend the case, but probably settle by giving Cain his $100,000 expected value. By settling the middle class Abel walks away with $400,000 and avoids the 20% risk of losing everything. If Cain won't settle for the expected value, Abel takes the case to court. If he wins he gets all the money and if he loses he is still middle class. The poor Abel will view the $500,000 potential inheritance as life-changing. He really does not want to walk away with nothing and continue being poor. He will settle by paying Cain somewhat more than the $100,000 expected value in order to eliminate the small risk of receiving nothing. Poverty makes for bad bargaining positions.

The expected value of a will contest is easy to figure if you can agree on the probability of success. In the real world, however, that seldom happens. Both sides think they have iron clad cases. In a subsequent post I will address the role of contingency fees on the math of will contests and then I will write about some factors that lead us to mistakes in determining the probability that a case will succeed.