1. Two (Three?) Games Philip Rash, NCSSM 2016 Teaching Contemporary Mathematics Conference

2. Two (Three?) Games Overview: Game #1 (Bigger Exponent) Game #2 (Biggest Product)

3. Game #1

4. “Bigger Exponent” – What’s the best strategy? Game #1

5. “Bigger Exponent” – What’s the best strategy? Game #1

6. Game #2

9. Two (Three?) Games So, it seems the answer is always “three”! But what’s so special about 3?

10. Game #2 – Continuous Version

16. “Bigger Exponent” Two players simultaneously write down two positive real numbers. The number a player writes down is the base, and the opponent’s number is the exponent. The player with the higher value wins. What is the best strategy? Why? Game #1 – Continuous Version

22. Game #1 See any resemblance?

24. Two (Three?) Games So, it seems the answer is always “three”!

25. Two (Three?) Games

26. Philip Rash, rash@ncssm.edurash@ncssm.edu http://www.ncssm.edu/tcmconference What’s So Special about 3?, Debra K. Borkovitz, Mathematics Teacher, Vol 108 No 1, August 2014, pp.71-75.