In the first two parts about how the format changes the strategy of winning daily fantasy sports I discussed the difference between tournaments and cash games and how tournaments you are looking to differentiate yourself with contrarian plays and in cash games you are looking for the wisdom of the crowd to help you win DFS cash games and maybe a few superior projections assuming such a thing exists.
Now I want to show how the format of tournaments and the example given regarding the dice roll can produce a positive result by doing something that on the source might seem very countertuitive... Playing against yourself and putting money on a losing bet to "cover all options". If you knew the field was unevenly distributed according to certain probabilities, there would be the potential to gain without trying to even handicap. Since in a given game you don't KNOW how many select 1,2,3,4,5,6 and which selections will be uncommon, we are going to show that betting $1 on all possible entries can be positive.
Rather than spend $1 with $1,000 entrants trying to guess the most profitable option of either a 1 or a 6, with KNOWN information about how others distribute their bets, you can simply distribute your bets according to probability. If an event is going to have a 1/6 chance of producing, you put 1/6th of the week's risk towards that outcome. You repeat for 100% of your capital. So the yield per $6 entry spent can be calculated based upon a distribution.
To review, the distribution of dice roll guesses is as follows:
50 people guess 1
150 people guess 2
300 people guess 3
300 people guess 4
150 people guess 5
50 people guess 6
You could randomize the actual number so that 300 people select 1 and 50 people select 3 as long as you have equally uneven betting, the strategy of betting on every single outcome is going to work. You profit to the degree by which opponent's error in their distribution. The mathimatically correct distribution is going to be 1/6th of a population guessing each number.
Given these assumptions, when a 3 or 4 are rolled, you only win $3.333. Since you only win this 1/6th of the time the "expected value" of making this bet is 3.333/6 which is $.55556. but remember, you paid $1 to place this bet so you've actually lost an average of $0.4444 for every dollar spent.
When a 2 or 5 are rolled, you gain 6.67. divide that by 6 and you gain 1.11 per dollar spent or $0.111.
When a 1 or 6 are rolled, you gain a whopping $20. Divide this by 6 and you gain $3.333 per dollar spent or a net gain of $2.333 per roll.
Add this all up and you end up with a net gain of $4 per every $1 risked! Think about that! By playing a game where you have a 1/6th chance of any outcome, and you bet 1/6th of your total bet size for the week on each and every possible option, you can win $4 for every $1 you risk simply by opponent's trying to guess an option that's consistently "close" rather than being a contrarian.
This strategy clearly doesn't work when there are only 3 options or only one single better. A rock paper scissors strategy isn't profitable unless it's a mass multiplayer version in which the profits of all the winners are added and losers are deducted and ties are split. If you are able to randomize your responses so you have each option 1/3rd of the time and the opponents end up disproportionally going with Rock, the tiems in which you go paper you are going to win more due to you facing more rocks than scissors. But the more people and the more uneven the distribution in representing equally likely outcomes proportionally, the greater the advantage, regardless of if you can actually identify it.
For those that are still unconvinced I want to give a specific daily fantasy sports example that contains a few core DFS principals that we will discuss later. One of the principals is "stacking", and another is "fading". For example, let's say you always pick a QB's less popular option and pair that player with the QB. There are a few reasons you might do this, but nevertheless, let's just say player A does this ONCE per week for 32 weeks. Player B does this 32 times in week 1. Who has a better probability of getting the highest scoring QB for the cost of 32 entries? Clearly the person who has 32 entries with 32 different QBs has a 100% chance of getting the best QB. It's very important to understand that with massive player pools the payout is so massive but competition is so heavy that you have to get the roster almost exactly right, so getting close might still return significant value but because of this, maximizing your odds of getting the exact right answer over the same cost is valuable.
While this player does NOT have any chance of getting the best combination more than once, he also is certain to have the 2nd, 3rd, and 4th highest scoring QBs, and if any one of those QBs connect with multiple TDs to an underowned, cheap WR, that player has a shot with the remaining roster of doing very well. Because it's rare for a WR to have a top performance without his QB having a top performance and because "getting CLOSE" to the best roster isn't enough, you want to STACK QB and WR combos mostly all of the time in tournaments.
A player who picks all, or a vast majority of entries adds value. I am not sugesting you should enter an insanely large number of lineups every single week, although a lot of the winning players do, but I am saying to at least do enough to cover a lot and cast a wide enough net each week. You're better off playing at smaller buy in games like $1 and $2 where the competition is lower quality and the payout per dollar risked is probably better 10 times than $10 or $20 once. in a given week.
The value comes from all of the similar lineups by your opponents that unfairly and disproportionally stack their lineups to the seemingly "best options" if the goal were simply to have the highest accuracy rate possible in having a relatively average to above average lineup 50% of the time. But remember, the payout is super massive if you win, so you instead should be okay losing several times in a row before you hit and you can be very very profitable.The goal is not to try to win every entry, but just increase your chances and value when you ARE hitting on your picks, and have your chances be stronger of hitting on those picks than the field allocates to those picks. (I.E. if you identify a player with a 5% chance of 'success' and less than 5% of the people have him on their roster he adds value despite a low probability of him succeeding).
When you have a lineup that is similar to everyone else, just as in the dice roll example, you don't win as much, but more accurately you are competing with a much higher amount of people. For example, if there are 100,000 entrants and you go with the two most popular options that occur maybe 40% of all rosters each, when this player does as expected you still have 9,000 remaining opponents that are EVEN in score when you hit the top combo and even then there are 91,000 others where 1/3rd has one, 1/3rd has the other and many of the remaining 1/3rd either aren't too far behind or have enough salary cap room that they are able to catch up by getting many highly talented players that are more likely than your remaining players to do well and can easily "close the gap".
But if you get say 32 QBs and mostly pick any WR, you have maybe a 20% chance on a given week of having the very best QB and best WR combo and are competing with the remaining positions, typically a lot more salary cap, AND everyone that picked the obvious choice at WR is pretty much out of the running. If your QB is NOT throwing to the obvious choice at WR and instead the other guy, that means that not only on good weeks you will be in the running, but also that the popular choice will be basically OUT of the running. Anytime someone pays a premium price for a WR who fails they aren't going to be very likely to win.
Aside from a 20% chance of having the best QB with his best WR combo (assuming your WR has a 20% of being the top receiving scorer of the offense), you have about a 67% chance of having at least one of your top 5 QBs connect with your WR you paired with him as his top scorer. The odds are quite good that you will find substantial value in covering your bases and stacking. If there aren't so many entrants and such a huge price for first proportional to the bankroll, you wouldn't want to make contrarian picks like this and you wouldn't have as many entries that are so unique and you probably wouldn't pair a QB/WR combo.
The only QBs you might make an exception on are the QBs with lots of target and a tendency to spread the ball around and for no option in that offense to score multiple times and be the focal point, particularly if the QB also gets a lot of his points from running as well. I probably wouldn't stack Kaepernick or Russel Wilson or Teddy Bridgewater for various reasons, but mostly a strong running game, strong defense and QB running ability makes it much more challenging for any one player dto do very well. It isn't like if a player is double covered and shut down the offense will only target a second or third option. The QB can run, the team can hand the ball off a lot and there are multiple options that all are equally viable who will receive a mixture of passes.
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