Circa Survivor – Week 18: The End

Circus Master took the Browns as expected.  He was the only one able to take the biggest favorite available in the pool.  I am sure he did not think too hard about that choice.  The others had more challenging decisions.

IndianaJet, JAX JAGS, and LAJONESER were all looking at a very similar situation.  When the picks needed to be in, they each had the same three teams as their largest favorite to choose from.  Denver, Houston, and Indianapolis.  Amazingly, they each chose a different team.  IndianaJet wound up in the best spot of the 3 as the Texans moved to a -5 favorite at game time.

As the math showed us last week, being on different teams with the same chance of winning was good news for all of them.  It was terrible news for Circus as he significantly lowered his chances of winning the pool that week.  As it turned out, all 4 were on different teams, and all four advanced.  That was a long shot to happen, but it did.

They could have done this intentionally if they cut a side deal to split the pot four ways.  There is a rumor that that has happened, but it is unclear when the agreement was made.  As stated last week, Circus was in a favorable spot, and an even split did not serve him well.

If we did not have a split going into this week, how should these players play it?

From the probabilities, the Bengals seem to be the obvious choice.  Each player has 25% of the $9,267,000 prize pool in equity, which is $2,316,750.  If they all take the same team, then we know the equity stays the same.  That could be a likely scenario if they were not taking a split.  New Orleans, Green Bay, and Detroit all have similar win probabilities at the time of this writing.  Would it be beneficial for one of these players to get off of Cincinnati and onto one of these teams?Let’s use LAJONESER for this example, as he is the only player who can take Detroit.  If he were to take Detroit and be up against 3 Cincinnati picks, does his EV increase?

The calculation is not difficult.

Multiply the probability of each event happening to find out what the probability of each scenario will be.
The four possible scenarios are as follows.

Cincinnati Wins & Detroit Wins = 69.9% * 60.2% = 42.1%
Cincinnati Wins & Detroit Loses = 69.9% * 39.8% = 27.8%
Cincinnati Loses & Detroit Wins = 30.1% * 60.2% = 18.1%
Cincinnati Loses & Detroit Loses = 30.1% * 39.8% = 12%

If you did the calculations correctly, it will add up to 100%

To calculate the EV, we simply multiply how much you will make or lose in each scenario and then add them up.

Cin W & Det W = 42.1% * $2,316,750
Cin W & Det L = 27.8% * -$1000 (entry fee lost)
Cin L & Det W = 18.1% * $9,267,000
Cin L & Det L = 12% * $2,316,750

This gives us an EV of $2,930,410.75.  So the play, if we knew everyone else was going to be on Cincinnati, would be to take Detroit.

The key is to be the only one on a team IF the rest of the pool is on the same team AND there is more than one opponent.  If you are in a heads-up situation in your pool right now, you are blindly taking the largest favorite and hoping your opponent tries to get cute and take a lesser team.  When you move to three people left in your pool, you would benefit from being a solo entry if the other two were on the same side.  But they may also know that, and perhaps one will take the team you take.  In which case, you gave player three the advantage you were trying to get, and they may be on the best team that week.  The fewer left in your pool, the more you will want to err on taking the chalkiest pick.

The math is the math, but we do not play the game in a vacuum.  It can be nearly impossible to predict what your opponents will do.  These pools become a sort of Prisoner dilemma game.  There are many ways to play the game, but ultimately, cooperating is the best long-term strategy.  You have the option to cooperate by taking a deal, hedging your picks, or a combination of the two.  This will be the best strategy in the long term, even though you are sacrificing a chance at the bigger payday.

Whatever you decide to do, congratulations if you are still alive.  Thanks again for following this article.  You can catch me on X @statsational.

Best of Luck in 2024!