Two Examples: #1. We flip coins for a dollar a flip. I start with $2, and you start with one. Algebra tells us that I will bust you twice as often as you bust me. Pure logic points out that this must be so since fair bets must break even if we do this every day. #2. I flip then you then me until one of us gets a head. Since I’m going first, math types make me 1/2 + 1/8 + 1/32……Smarter people realize that on the first round I’m 1/2 and your’e 1/4 and that ratio remains on all rounds until there is a winner. We both get 2/3.
No further explanation needed. All comments welcome.