Continued from part 1...
If you go along with the other 4 competitors and use team A as your pick, then a 5 way tie for 1st place is guaranteed and you will get 20% of the $100 prize pool.
Can picking one of the other teams, with less of a chance to win their game actually lead to higher expected winnings? Let's find out.
If you pick team B instead of team A, then you will still finish in a 5 way tie if both teams win or both teams lose. As stated in part 1, team A has an 80% chance of winning and team B has a 70% chance of winning. The probability that both teams win is 80% * 70% = 56% and the probability that both teams lose is 20% * 30% = 6%. So 56% + 6% = 62% of the time you will still finish in a tie and win 20% of the pot even though you picked a different team.
If team A wins and team B loses, you, of course, will win nothing. This will happen 80% * 30% = 24% of the time.
But, in the event that team B wins and team A loses, you will get 100% of the prize pool all to yourself. This will happen 20% * 70% = 14% of the time.
So to summarize, 62% of the time you will get 20% of the prize, 24% of the time you will win nothing, and 14% of the time you will win 100% of the prize pool. To calculate the total expected winnings, you take the sum product of the probabilities of each case and the winnings from each case: 62%*$20 + 24%*$0 + 14% * $100 = $26.4. $26.4 is more than $20 so picking team B, which actually had a lower chance of winning than team A, is the best strategy here.
| Case | Probability | Winnings | Expected Winnings |
|---|---|---|---|
| A & B win | 80% * 70% = 56% | $20 | $11.2 |
| A & B lose | 20% * 30% = 6% | $20 | $1.2 |
| A wins & B loses | 80% * 30% = 24% | $0 | $0 |
| B wins & A loses | 70% * 20% = 14% | $100 | $14 |
| Total | 100% | - | $26.4 |
Before the start of the weekend, the distribution of picks across all 32 possible winners is published by sites such as Yahoo! How can this information be used to increase your expected earnings similarly to in this example? Let's tackle that in another post. To be continued...
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nice deduction! unfortunately, this leads to a suboptimal nash equilibrium, as everyone will end up doing this, giving you all $5.48. i know you assume they don't, but that's like assuming a raft!
ReplyDeleteI am not a math genius. I would not have been able to come up with such a deduction. All of that being said, I would have picked B purely out of greed. If I know that the other contestants all picked A, rather than split the pot 5 ways, the gambler in me would want to win the whole thing....therefore I would have picked B. I would have also realized that chances are that both teams win anyway.
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