Secrets of the CelticsHow to win at SDG without cheating

Christopher Chalifour Duc Tri LeThomas Pappas

Inspiration:  The Super RobotFrom an email sent by Professor Lieberherr on 02/07/09

• "That robot will soon be the only one alive because it saps much life energy from the other robots."o  Guaranteed win?

• "Even if the other robots don't buy from the super robot because they are "afraid" of her, the super robot will spot all good food in the market and will have the life energy to get it. "o  Perfect buying decisions

• "In addition, ...  super robot can accumulate life energy with lots of small profits."o  Small, constant profits

Performance of the Celtics

• 47 deliveries of RawMaterialso Made a profit on all of them

• 35 purchases of Derivativeso Only 2 ended up as a losso Small loss of 0.021 & 0.043

• 58.185 seconds spent entire gameo 6 roundso 2 overtime rounds

Source: http://www.ccs.neu.edu/home/lieber/courses/csu670/sp09/alex/competitions/mar10/4/history.html

Our Success    What gave us the winning edge?

• Knowing the best price to buy derivatives• Knowing the best price to sell derivatives• Knowing how to create tough raw materials• Knowing the best price to re-offer

derivatives

Pricing A DerivativeHalving the Min-Decrement - Bender's Concept

• Forces the selling robot to price the derivative with this price as anything higher allows another robot to price their derivative at the "perfect price" resulting in our robot losing it's potential to make a sale and thus, make a profit

• Forces an opposing robot to re-offer the derivative with a lower price of at most P = (Break-even - ½ MinDec)o Finishing this derivative at a break-even price causes the selling

robot to still lose ½ MinDec• Forces an opposing robot buying this derivative to

lose ½ MinDec by finishing at a quality of at most break-even

The Perfect Price = (Break-even + ½ MinDec) 

Creating a Tough RawMaterialMethod #1

• Each Constraint will have a weight of 1• Number of Constraints for each RelationNr =

Weighted fraction of RelationNr x Maximum number of Constraints

• A good RawMaterial but not truly symmetric

Creating a Tough RawMaterialMethod #2

• Remove RelationNrs with a weighted fraction of 0

• Divide the number of Constraints evenly among the remaing RelationNrs

• Assign appropriate weights to Constraints so that weighted fraction will be satisfied

• Better most of the time but not all• There is really no such thing as a perfect symmetric

RawMaterial!

Why "Break-Even" is broken(Credit to Xueyi Yu)

• "Because from what I observed from the competition, a Robot can finsih a raw material with a quality > breakeven"o Xueyi Yu

(02/19/09)

Mentioned over email... As taught in class...• Break-Even is the

highest possible finishing Quality given the worst possible raw material.

• Calculated through using a Look-Ahead Polynomial

A Real-World look at Break-EvenUnused / Outdated Documentation

• This data for this example is taken from the class website, shows how the more constraints, the closer the max Quality is to the Break-Even.

• Look-ahead polynomials assume infinite constraints.

Finished Quality = 0.4679802... for 10 constraints

0.4466790... for 100 constraints

Break-Even =  .444444...

Why focus on the delivery of RawMaterial?

• We used actual qualities to make decisions rather than break even prices

• The tougher the RawMaterial, the better we know of the worse case scenario

• So we know that the chance of someone finishing better than what we priced is slim

• When buying, if the worst case is higher than the Derivative's price, we know for sure we can make a profit

SummaryThe Perfect Robot

• Makes all decisions based on profito Wont create derivatives that sell for a losso Will almost never buy derivatives for a losso Will never re-offer derivatives for a loss

• Only guaranteed for a 1-on-1 scenario