Secrets of the Celtics
How to win at SDG without cheating
Christopher Chalifour
Duc Tri Le
Thomas Pappas
Inspiration: The Super Robot
From 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 RawMaterials
o
Made a profit on all of them
• 35 purchases of Derivatives
o
o
Only 2 ended up as a loss
Small loss of 0.021 & 0.043
• 58.185 seconds spent entire game
o
o
6 rounds
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 Derivative
Halving the Min-Decrement - Bender's Concept
The Perfect Price = (Break-even + ½ MinDec)
• 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
Creating a Tough RawMaterial
Method #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 RawMaterial
Method #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)
Mentioned over email...
• "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)
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-Even
Unused / Outdated Documentation
Finished Quality =
0.4679802... for 10 constraints
0.4466790... for 100 constraints
Break-Even = .444444...
• 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.
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
Summary
The Perfect Robot
• Makes all decisions based on profit
o
o
o
Wont create derivatives that sell for a loss
Will almost never buy derivatives for a loss
Will never re-offer derivatives for a loss
• Only guaranteed for a 1-on-1 scenario