GeekDad Puzzle of the Week Answer: Soccer Wars

The end of spring break is near and with the end of break, we'll be back to YMCA soccer season. Did you help save the soccer season, dear GeekDads? The answer is yes, mostly. Perhaps it wasn't my cleanest puzzle or perhaps a high percentage of GeekDads, like me, were too busy being beaten with padded swords for this week of spring break to put together an entry, but we were a bit light this week. So consider this a calling out for Judd's puzzle on Monday.

In any case, here was this week's puzzle:

I wonder what is the best way to order kids on the field to maximize the chance of the ball happening to flow forward through this string and into the opposing (and not our own) goal?

Picture the soccer field as five boxes, stacked in a line, with nets just off the grid at either end. Imagine that an opposing player has an equal chance of bringing the ball into each grid space occupied by one of our five players. Whoever is goalie stays in the back square and adds 10% to their "divesting" chance and has 90% chance of propagating the ball forward one grid space (and a 10% chance of accidentally kicking it into our own net). Otherwise, each player kicks the ball according to the following rules:

• Leif: 50% chance of divesting an incoming, opposing player; 50% chance of propagating the ball one grid space; 25% the ball will propagate two grid spaces; (25% he will be divested before propagating); 80% the ball will travel forward from grid space; (20% it will travel backward).
• Kestrel: 10% chance of divesting (5% chance of biting opposing player); 90% chance of propagating one grid space; 5% of propagating two; (5% divested before propagating); 50/50 whether the ball travels forward or back.
• Bobby Big Kicker: 10% divesting; 10% one space; 50% two spaces; 10% three spaces; 60/40 forward versus back.
• Pamela Precision: 20% divesting; 70% one space; 90% forward.
• Erin the Enforcer: 80% divesting; 40% one space; 75% forward.

How should I order these five kids in these five boxes for the best chance of success?

This week's winner was Andy, who used Python script to find, "The ideal order is Erin (goalie), Pamela, Leif, Bobby, Kestrel" and then explained:

Qualitatively, this seems to make sense. One of the takeaways from my soccer-playing days is that the best way to score goals is to keep the pressure on by keeping the ball near your opponent's goal. This team does that pretty well. Erin is great at taking the ball from incoming players, so put her in the net. Pamela makes a good defender, because when she has the ball, she almost always moves it up the field, rather than back towards her own goal. Bobby's got the big foot, so we put him in position 4 - he has a decent chance of moving the ball up 2 or 3 spaces and getting a goal. Kestrel's weakness is her propensity to move the ball backward, but if we put her on the front lines, then even if she does go the wrong way, the ball probably goes to Bobby, who, as I said, has a decent chance of scoring a goal. That leaves Leif in the middle of the field, which makes sense because he's a good, solid utility player - he's not the strongest in any stat, but he's not the weakest either.

The rest of us can use the code GEEKDAD37MD to get $10 off a $50 order at ThinkGeek. Thanks for playing the puzzle!