Strange, are you a deliberate troll?
This is half a dozen threads of yours that I've read where you posit the obvious wrong solution and then proceed to defend it even against immeasurable evidence (and I believe you know you're wrong), presumably just to generate ire. It's getting old.
Check out the simulator link that rat provided:
http://www.grand-illusions.com/simulator/montysim.htm
Do "Run" 100 times as many times as you want, and select keep vs. change. If you can't see it, then this thread is over because you're simply not contributing.
Here are my results. Does that not look exactly like 2/3 and 1/3 to you?