Essay on Coin Flip Probability
by Tom Over-Being and Drogo Empedocles
Basically the odds of a coin toss in your favor are 1/2 right? 50/50 in other words, 50% of the time tails, 50% heads. It’s a function of how many times you toss the coin then, represented as (1/2) ^ x Where x is number of tosses. In the case of 6 coin tosses then it would be (1/2)^6 which works out to be 0.015625 or 1/64.
It is easy to understand that each time you flip a coin you are re-setting the odds. The previous result means nothing. So the fact that the chances of getting the same result over and over is not 50/50 is the weird part; as referenced in ‘Rosencrantz & Guildenstern Are Dead’ by Tomm Stoppard (Video clip). Each toss is supposed to be 50/50, but the odds of 6 results ending up one way is not the same math, and this may seem odd.
Tom O – “say I have a d4 (pyramid dice), It’s (1/4) if I toss it once, it’s (1/4)^1; if I toss it twice, and want to get “3” both times, the odds are (1/4)^2. Now with the dice the only thing that changes is the fraction coins are (1/2) dice are (1/6). Or another way of looking at it is say you have to make the best of 3 tosses. That’s the most equitable way to randomly make a decision if you don’t want to flip just once right? Well each time you toss that coin the odds of getting heads is 1/2.. You could also solve the problem by throwing 3 coins at once too right? Well that means you’ve run those odds (1/2) by themselves 3 times (1/2)^3 the exact same thing as tossing the same coin 3 times too.”
The odds of getting heads 6 times in a row are not 50/50, like in the Democratic Iowa Caucus of 2016 (‘lucky’ Hillary) that used coin flips in the ‘democratic’ process rather than votes; the odds of getting heads 6 times in row are 1-to-64 !!!
6 heads in a row = 1 / 64
12 heads in a row = 1 / 4096
24 heads in a row = 1 / 16.87million
Khan Academy – Probability & Statistics