[soop]

I play a fantasy world cup game. This puzzle doesn't necessarily have to refer to football, but that's the inspiration, and a neat enough way of explaining.

you have a team of 15 players, including 4 substitutes. After the group stage, it goes to the knockout stages.

There will be 16 teams, then 8, then 4, then 2.

Assuming I start with a full contingent of players when there are 16 teams, what is the best way to ensure as many players remain in your team for the final match, with as few transfers as possible (swapping one player for another)? I'm currently guessing, and placing my bet on teams like Brazil, but there should be a logical way to do this.

If you understand fantasy football, it should be fairly self explanatory, but if you don't and it needs clarification, just point out where I've been unclear

[Guest]

I'm not sure what your asking. How do you lose players? Surely if you start with 15 players you should have 15 at the end?

Edit: Oh I think I understand what your saying now. I'll have a go then.

Edit 2: It seems you want to optimize 2 variables. The number of players and minimize the number of transfers. You usually can't do this. Its one or the other really.

Edited June 21, 2010 by psychic_mind

[Quantum.Mechanic]

Please specify the number of games in the group round. Might as well specify the number of possible matches in the knockout tree.

I'd also like to know the rules for swapping players, etc. I have no experience with fantasy sports, though the puzzle sounds interesting.

[Guest]

here's the puzzle reworded for more thoroughness.

16 teams; each with 15 players; will play against each other, until only two are left (losing team eliminated after each round.)

you can pick 15 players from any team, 4 of which are "back-ups".

the goal is to distribute your picks such that the fewest players of the ones you picked are eliminated, and preferably no back-ups used.

for example:

i'll pick 2 players on teams 1,4,7,10,13, and 1 player for teams 2,5,8,11,14 (5,8,11,14 are my backups.)

round 1:

match:   winner:

1v2       1

3v4       4

5v6       6

7v8       7

9v10      9

11v12     11

13v14     13

15v16     16


round 2:

match:  winner:

1v7        7   (note the random pairings, for round 1 

4v6        4   this doesn't matter, but for round 2 it does.)

9v13       9

11v16      16


round 3:

match:  winner:

7v16      7

4v9       9

number of players left out of my pick: 2

make sense?

Edited June 22, 2010 by phillip1882

[Guest]

admittedly I've never done fantasy football, so I'm not sure how the back ups are handled; maybe you can switch them to a team that won if you lose them a round, I honestly don't know there.

[soop]

What will happen is that first of all 8 teams will play another 8 teams (8 matches); then the 8 winners will play each other (4 matches). The 4 winners will play each other (2 matches) before the decider between the final 2 teams decides the world cup winner.

As I will get points for everyone on my team, I need as many people as possible who won't be knocked out for as long as possible.

let's say my 15 players are made up of 1 player from each 16 teams bar one.

The next round, around half of my players will be knocked out (best case I will lose 7 players, worst case 8). Now I can transfer out the 7 or 8 players, and make another selection from the teams still in the tournament. I will have to choose players from the remaining 8 teams, so I could for instance choose 2 players from each team, apart from one team which I have one player.

Now if I do this, when those four matches have finished, I again lose half of my team, and need 7-8 more transfers.

This continues. It might not be the best way of doing things, and the best way may go into probability. It also may be better to find a way in which I can maximise the number of players rather than have a full contingent.

As for the substitutes, it might be better just to disregard this, and assume I have 15 players on my team.

[Guest]

Should we assume all teams have an equal chance of winning each game? Or are some teams better than others?

[Guest]

Well, I have never played fantasy footbal but on a lighter note, I think it is based on random events. If Spain which is a hot fav in Europe to win the WC can loose to switzerland, and Messi can't score in the two matches despite playing as good as he did, France crashes out in first round with just one goal in 3 matches, and England might just follow suit!!, i think picking players for fantasy football is as good as picking lottery tickets.

And it doesn't matter which players (read tickets) you pick, your chances do not improve too much by selcting one player (ticket) over the other.

I hope the comment does not ruffle too many feathers of the football crazy fans!