I think (some) people are confusing the

*a priori* expectation with the actual outcome.

Let's you and I play a game. You will flip a (fair) coin exactly 10 times and I win if it lands on heads

**all **10 times.

*A priori* (a statistics term meaning before the event or game has started) my chance (ie probability) of winning is exceedingly small. The exact probability can be calculated using the Binomial distribution (

@RainmanTrail Help????).

After the first 9 trials the result has been all heads (itself a very unlikely outcome but here we are). My chance of winning the whole game is now 50% (i.e. the 10th and final coin flip is a 50/50 chance). However unlikely I am to be in this scenario to begin with, the next coin flip is independent of what preceded it. This holds true (obviously) for rolling a die (1/6), black or red in Roulette (making these tracking systems somewhat curious), or hitting my two outer on the river (~5%).

Would you have predicted I would have won before we started? Probably not. Would you bet with me for the final flip? Probably.