Thinking Through 3-Player Contests

Thinking Through 3-Player Contests

DraftKings offers three player contests with a variety of entry fees. These entry fees range from $1 to $10,600. In these three player contests there is only one winner, who gets 2.7 times their entry fee as winnings.

There is a way of playing these contests to maximize your chances of growing your bankroll. Lets say you enter into one 3-Player contest. In order to make a profit you would have to win that one contest. Now lets say you enter into two of these contests. In order to make a profit you must win one contest.

You must always take into consideration the risk to reward ratio. There is no point in risking more money if you still need to win the same number of games in order to profit.

Here is an example that shows inefficient betting:

Lets say you enter 3 contests. Using the $1 entry fee as an example you have now risked $3 for a chance to win a maximum of $8.10. In order to make a profit, you must win at least two of the contests you entered. This means you must win 66% of your entered contests in order to profit. Since each contest has a 33% chance of you winning, on average, this is a losing strategy.

Let's assume you do good research and have reliable projections for you lineups. Your winning percentage will be closer to 40% than 33%. So how many lineups should I enter in order to maximize my chance to profit?

Here are two examples that show efficient betting:

Lets say you enter into five $1 tournaments. You need to win two out of the five contests in order to make a profit since 2 x $2.70 = $5.40. So you only need to win 40% in order to make a profit, which is much better than the previously stated 66%.

Now lets say you enter eight $1 contests. Doing the same calculations as before, you will need to win 37.5% of the contests in order to make a profit.

Will you ever get odds better than 37.5%? The chart below shows the percentage of contests you must win in order to turn a profit based on how many contests you enter.

So will the odds ever get better than 37.5%? Yes, after running a computer simulation for the first 100 contests entered, I found that if you do the math for playing in 27 contests the percent drops to 37.03%. This is the lowest that the percentage will drop. Another way of finding this number is to remember that for ever dollar you put into a contest there is the possible return of $2.7, and 1/2.7 = 37.03%.

What should you do with this information?

If you have good projections, and you do your hockey research, it is possible to have a winning percentage above 37%. This means it is possible to be a winning player playing 3-Player contests. Assuming you don't want to go to the trouble of playing 27 different contests, you are better off playing in eight different contests. The difference between 37% and 37.5% is not that much so you will still have the odds stacked in your favor.