Doc Holliday versus Ike Clanton (2-person, 3-strategy game) are used in this problem. On October 26, 1881, the bad blood between the Earps, Clantons, and McLaurys came to a head at the O.K. Corral. Billy Clanton, Frank McLaury, and Tom McLaury were killed. Doc Holliday, Virgil and Morgan Earp were injured. Miraculously, Wyatt Earp was unharmed, while the unarmed Isaac ``Ike'' Clanton survived by running away. Many people believed that Doc Holliday shotgunner an unarmed Tom McLaury in the back as he was attempting to flee the scene.

Ike Clanton and his friends and associates, known as the ``cowboys,'' swore to get their revenge on the Earps and Holliday. In the ensuing months, Morgan Earp was mur- dered and Virgil Earp seriously wounded in an ambush. A few days later, Wyatt Earp apparently shot and killed Frank Stillwell, a Clanton associate, and another man believed to be involved in the ambush. Over the next few years, many more of the cowboys were killed.

Although close to death from tuberculosis, in 1887 Doc Holliday decided to look up Ike Clanton and to settle their differences once and for all. On June 1, 1887, Doc Holliday and J. V. Brighton cornered Ike Clanton near Springerville, Arizona. Doc told J.V. to stay out of it for the time being.
Ike and Doc each had a pistol and shotgun. Ike and Doc, spurning their pistols in favor of their shotguns, pressed forward toward each other. At long range, Ike—with his cowboy background— was a better shot than Doc. At middle range, Doc—the seasoned gunfighter could outgun Ike. Both desperadoes were deadly at close range. The probabilities that either rogue would kill the other with a blast from his single-shot shotgun appear in the following table:

In this problem, the payoff to Doc is 10 units if Doc survives and Ike is killed, –10 units if Doc is killed and Ike survives. Doc and Ike's strategies are as follows: