A STRANGE Deal with the Devil

Strange #1 by Mark Waid and Emma Rios (2009)

Here's a piece of advice that might help you in the future: do not, under any circumstances, make deals with the devil. It is always either a trick, an information paradox, or just not worth it. The devil always has something up his sleeve to make sure that the benefits of the transaction are skewed towards his side. That's why he's the devil.

Of course, if you're dealing with one of the devil's lackeys, you might find it beneficial. Such is the case with Strange #1.

The Pitch

In this issue, the Portland Loggers, a crummy baseball team always at the bottom of the League, are offered a chance at success by a demon named Tul'uth:

The terms are as follows: the Loggers are guaranteed to win 66.6% of their home games for the span of 30 years. After this time, all team members must then surrender their souls for all eternity (this part is non-specific, but I think this is what is meant by giving up souls).

Let us now make the following assumptions:

1) Each player is rational. He only cares about his own utility and not that of the others (making him a poor team player!).
2) Without less of generality, we can assume that at any given time the Loggers have a roster of 25 players and that Tul'uth offered 25 years of success instead of 30.
3) Each player values his soul at 10 years of success.*

*Note that we really have no way of knowing how each player equates souls and baseball victories. Yet, I don't think it's a stretch to assume that a soul is worth more than 1 championship. We also know that the value of a soul cannot exceed 30 championships (25 in our modified case), otherwise the team would not have taken the deal.

The interesting thing about this scenario is that Tul'uth is framing the deal in a way that incentivizes the Loggers to accept. What's more is that they would benefit by doing so. But it doesn't have to be this way. Suppose instead he offers an additional year of victory for every soul given to him.

Let's say that he offered this deal only to Player A. In other words, Player A could give up his soul for a division championship that year. Well, since Player A values his soul more than the utility of 1 championship, he would not take the deal. The other players on the team, however, would want Player A to take the deal, since then they would benefit from the victory without sacrificing any of their own souls (free riding). Unfortunately for them, Player A doesn't care about what they want. No deal.

In fact, if all the players were offered the deal in this way, it would pretty much be a standard prisoner's dilemma scenario. If each player took the deal, then the team would win 25 championships. Yet, each player would sacrifice the equivalent of 10 championships (1 soul), netting a total of 15 championships each.

Now let's say that Player A got wise and decided he would rather keep his soul and free ride on the others. If he defected from the group, then the entire team would be docked only 1 championship. However, Player A would get to keep his soul, which we know is worth 10 championships. For him, this would yield a net of 24, which is greater than 15 (the benefit of taking the deal).

So we see that under these assumptions, it is possible that no player takes the deal and the Portland Loggers continue on their losing streak. Tul'uth prepared for this, however, by offering a different deal. In effect, he dissolved this free rider problem by restricting the deal to either 25 years for 25 souls or nothing at all. By forcing each player to pay, he modified the choice to being between 15 championships per player or 0. Clearly, each team member would elect to take the deal.

The Catch

If you're wondering if there's a clever demon catch, there is. The catch is that these ball players have no arithmetic skills. In a baseball season, each team plays 162 regular season games. Half of them are home games. So, in one year, the Loggers would play at minimum 81 home games. If, through Tul'uth's deal, they were guaranteed to win 2/3 of these games, then they would win at least 54.

But this alone is not enough to qualify the Loggers for division championship. They'd need considerably more wins. Doctor Strange mentioned that the Loggers were consistently the worst team in the league. Let's assume that they typically lose around 100 games a year, which translates to 38% winning games. If we assume the Loggers win 66.6% of home games (54 games) and apply the 38% that they would win on their own to the remaining 108 games, then this would guarantee 95 wins. This would surely put the Loggers in good standing for division championship, but it would certainly not be a guarantee.

And this is being generous. It is entirely possible that the Loggers have a worse average annual record than 62-100. Further, this is assuming that we can even apply the 38% to the remaining games, which would not be the case if Tul'uth's 66.6% included some home games that the Loggers would have won on their own anyway.

The Out

At this point, you might say, "Aha! So the Loggers are screwed." But as it turns out, there is another caveat in the contract that makes the deal is more generous than it looks.

What a twist! The Portland Loggers don't even have to give up their own souls. The contract actually stipulates that the beneficiaries are defined as "the home team" and not the individual players who made the deal. Therefore any team, regardless of composition or name, is held accountable to meet it end of the bargain so long as it occupies the old Loggers stadium.

So, what we have here is a situation a demon has given some people the ability to sell other people's souls. They could each, theoretically, play baseball for 24 years, receive 24 championships, move or retire on the 25th year, keep their souls, and let some poor suckers pay the burden for all eternity with none of the reward! How horrible for those suckers, but how unbelievably awesome for the original beneficiaries.

This begs the question of what exactly Tul'uth's intent was here. If he was dead set on securing the souls of the original Portland Loggers (i.e. the team that made the deal), he sure picked a silly way to do it. It's true that this squad was not aware of his contractual nuance, so you might be inclined to think they just got lucky. However, it is very rare for a team to remain intact for 25 years. Even supposing that all of these players would still be playing baseball after 25 years, players get traded all the time beyond their control. Tul'uth HAD to have anticipated that he would not score this original team's souls.

In fact, Tul'uth is the one that got lucky. The Loggers went broke and the stadium shut down for many years. If not for the new team that began using the old stadium, he would have been left soul-less after the contract expired. So why did Tul'uth not simply make the deal for the players' souls?

It could just be that Tul'uth didn't particularly care which souls he got so long as he got some. But then wouldn't it have been simpler to ask the Logger to just, I don't know, pick some other souls?

All in all, an oddly generous deal coming from the "lord high incubus of games and chance." He offered them all the benefits of victory with the ability to void the contract after the fact. AND they didn't even have to know about it!

This is why the devil should do all his deal-making himself and not rely on some hack subordinate. Score one for the home team.