Let's play a hypothetical game of rock paper scissors (officially named "roshambo"). In rock paper scissors, what we call the theoretically optimal strategy doesn't actually have an edge. But you can completely neutralize the edge opponents have over you by randomizing your response. Contrast this to someone who always goes "paper" and never changes strategies. This is easily exploited over time by people who figure this out and always go scissors, or at least go scissors far more often than 1/3rd of the time to give the illusion to the player that they have a chance at their strategy working. The problem with strategies that try to exploit opponent's strategies is that there is the possibility of deception.
What if a player "Bob" initially assumed that an opponent won't usually doesn't go paper twice in a row but after 3 paper's in a row assumes their opponent is using an "always paper strategy" and counters with an "always scissors" strategy? furthermore, what if BOB always starts out rock, assumes that anyone who goes paper will go back to scissors, and then if there are two papers in a row, certainly the opponent will go to scissors the 3rd time. If an opponent KNEW that Bob always operated this way they could counter-exploit, by going 3 papers and then rock. The point of this is showing how any strategy that attempts to exploit weaknesses are vulnerable to their assumptions being wrong.
However, there are other games in which the perfect strategy CAN be profitable if opponent makes a mistake. Take for example a dice role in which the closest guess wins. There are only 3 answers that have the potential to show a profit in the long run vs a single opponent. A 3, a 4, or a fraction between 3 and 4 such as 3.5. With a guess of 3.5 you are never exactly right, but you are never more than 2.5 off of the correct answer. You are within 1.5 or less 50% of the time. Even if thousands of players played this game, as long as it paid the top 50%, you should probably guess a 3,4, or 3.5. Your profit comes from people who guess a 1, a 2, a 5, a 6 or a fractional number above 4 or less than 3.
However, what happens if we change the payout from the top 50% to the top 20%? Or what if only those who get the number exactly, or nearly exactly right split the prize pool? Now guessing 3.5 becomes foolish, and actually guessing a 3 or a 4 while frequently close, and equally as likely to be correct as any other single number actually becomes a poor choice if you expect the vast majority to play to be "close" and guess a 3 or a 4.
Let's prove this by an example.
50 people guess 1
150 people guess 2
300 people guess 3
300 people guess 4
150 people guess 5
50 people guess 6
Those that guess the prize pool exactly right split the profits with the remaining field.
So if you pay $6, let's look at the possible outcomes
1,6: you win $1000/50 people 1/6th of the time each (1/3rd total).
2,5: you win $1000/150 people 1/6th of the time each (1/3rd total).
3,4: you win $1000/300 people 1/6th of the time each (1/3rd total).
This type of distribution is actually fairly common, and fairly rational. Afterall, those who guess 3 and 4 are going to be closest to accurate most of the time. But unlike in a cash game where you only need to be better than half the field, you need to be EXACTLY right on at least a handful of positions, or very close to exactly right on all of them.
Please don't depend on me explaining it to you entirely and stop now and reflect on all of this and try to extrapolate this information to fantasy football daily games.
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(you did stop and think about it, right?)
/end of reflection
We can obviously see that it pays to be a contrarian PROVIDED the odds of the outcome occuring is greater than the percentage of people who guess that outcome.
That same knowledge applies to daily fantasy games in that in these large contests you have to get your roster close to exactly right, and as such, the probability of the player scoring the most points at his position must exceed the percentage of players who selected that player. Note: We can complicate things if we want to be slightly more accurate since a player who does not score the most points at the position but is the cheapest and still scores among the top may actually have more value IF those salary cap dollars can be put to work to produce a better roster. However, whether you define the "best" as the most points, or the most points per dollar of salary cap or some blend of both isn't as important as understanding the concept. It often pays to be a contrarian.
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