Coin Toss Odds Explained

Calculating the coin flip odds should be easy enough. Especially since when tossing a coin there are only two outcomes possible. Assuming you don't have a trick or weighted coin getting heads or tails is equally likely. However, things get slightly more complicated when adding multiple coins to the equation. If two coins are tossed there can only be two heads, two tails or heads and tails so there are three possible outcomes, right? Actually, that isn't the case since you have to think of the outcomes for each coin separately. There are actually four possibilities. Since you can have both coins come up as heads, both coins showing tails, the first coin a head and the second coin a tail, or the first coin a tail and the second coin heads.

For each additional coin the possibilities are multiplied and the coin toss odds change. For one coin there are two outcomes, for 2 coins there are 2x2 or 4 outcomes, for three coins there are 2x2x2 or 8 possible outcomes.

Once you know the number of possible outcomes you can easily predict the coin toss odds. Let say we have three coins and we want to calculate the coin flip probability for getting only one head (and so two tails). Here are all of the possible coin combinations: HHH, TTT, TTH, THT, THH, HTT, HTH, HHT

Since there are 8 different possibilities but only 3 outcomes that have one head showing we can calculate that the coin flip odds are 3/8 which equals 0.375 or when written as a percentage 37.5%.

To calculate the coin toss odds for any other result the method is the same. Count the total number of possible results and the number or results with your criteria. Divide the favorable results by the total results and you'll have the coin toss probability you were looking for.

If you want advice on which side of the coin to bet on here is a little tip. The best bet is to pick the side which is face up before flipping as there is a slightly higher probability (51%) that it will land on the same side that it started on. The reason given for this it that coins don't always spin perfectly around through the air and sometimes appear to flip when haven't. This theory only works for situations where the coin will be caught in the palm of the hand and not permitted to bounce. There are also those who say that more often than not pennies will land on heads because of the way they are minted. The face of Lincoln protrudes more which weights the penny causing a change in the coin toss odds.