What are the odds?

If you read this blog regularly, you may remember my probability post concerning the roll up the rim to win Tim Horton's cups. At the time i posted it, i was running at a winning cup every two drink purchases. Since then, i haven't seen a single winner in 13 cups (unlucky??). At first glance, it would seem that i have had a run of bad luck. But when you look closely at the numbers, and compare them to the stated odds of Tim Horton's winning cups (1 in 6 this year), it would seem that i could have easily anticipated my string of 'bad luck'.

Right now i sit at 2 wins out of 17 cups. Taking the 1 in 6 odds that Tim Horton's advertises, one might think my next purchase should very well be a winning cup. 1 in 6 odds would mean 3 wins for every 18 cups purchased. However, by that logic, could i potentially not see a winning cup until the 23rd cup purchased, followed by a second win in a row at cup number 24??? This would still give me 1 in 6 odds, should the 23rd and 24th cup prove to be winners.

So next time you think you've hit a run of bad luck, or a jackpot of multiple winners, remember the math behind it all, and that the odds were right there in front of you the entire time.