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# Tournament Sports Betting

## Question

64 teams are going to play in a tournament. You desire to bet your \$192 savings on these teams but you know absolutely nothing about these teams so you will use a fair coin to select the team that you think will win the contest. Every correct bet doubles your money so a \$1 bet awards you back your dollar plus an additional dollar and you cannot bet on two teams if they are playing each other in the same round.

The tournament is a single elimination contest, hence there will be 6 rounds. Your goal from betting is to attempt to make the most money at the end of the tournament.

You have two friends who proposed betting strategies:

Jon says that you should bet \$32 for each round evenly. So in the first round, you put \$1 on each team you think will win, then in the second round \$2, culminating the final round with \$32 on the winning team.

Eric, on the other hand, says you should bet \$3 on each team in the first round, \$3 on each team in the second round, and so on.

If you bet on the same teams regardless on the strategy chosen, which strategy will produce the most money?

## 1 answer to this question

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Some thoughts - unless I am missing something

in round 1, there are 64 teams in 32 games. If you choose randomly, you should win about half the games [16 in round 1] for each win you will get your bet back + that same amount [2*\$bet].

Using Jon's strategy [doubling the bets every round]

you bet \$1 on 32 games [\$32 outlay], ------------ win half the bets [16] and get twice your bet [\$2] for every win or 16*\$2 = \$32 ...... break even

Round 2: bet \$2 on 16 games [\$32 outlay],------ win half the bets [8] and get twice your bet [\$4] for every win or 8*\$4 = \$32 .......... break even

Round 3: bet \$4 on 8 games [\$32 outlay],------ win half the bets [4] and get twice your bet [\$8] for every win or 4*\$8 = \$32 .......... break even

Round 4: bet \$8 on 4 games [\$32 outlay],------ win half the bets [2] and get twice your bet [\$16] for every win or 2*\$16 = \$32 .......... break even

Round 5: bet \$16 on 2 games [\$32 outlay],------ win half the bets [1] and get twice your bet [\$32] for every win or 1*\$32 = \$32 .......... break even

Round 5: bet \$32 on 1 games [\$32 outlay],------ win half the bets [0.5] and get twice your bet [\$64] for every win or 0.5*\$64 = \$32 .......... break even

By my calculations, you walk away [on average] with the same amount of money you started with using Jon's strategy

Eric's strategy [\$3 on every game]

Round 1: bet \$3 on 32 games [\$96 outlay], ------------ win half the bets [16] and get twice your bet [\$6] for every win or 16*\$6 = \$96 ...... break even

Round 2: bet \$3 on 16 games [\$48 outlay],------ win half the bets [8] and get twice your bet [\$6] for every win or 8*\$6 = \$48 .......... break even

Round 3: bet \$3 on 8 games [\$24 outlay],------ win half the bets [4] and get twice your bet [\$6] for every win or 4*\$6 = \$24 .......... break even

Round 4: bet \$3 on 4 games [\$12 outlay],------ win half the bets [2] and get twice your bet [\$ 6] for every win or 2*\$6 = \$12 .......... break even

Round 5: bet \$3 on 2 games [\$6 outlay],------ win half the bets [1] and get twice your bet [\$6] for every win or 1*\$6 = \$6 .......... break even

Round 6: bet \$3 on 1 games [\$3 outlay],------ win half the bets [0.5] and get twice your bet [\$6] for every win or 0.5*\$6 = \$3 .......... break even

Thus Eric's strategy results in an average gain of \$0
Bottom Line: neither approach will on average net you any money - both are equally good [bad].

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