The tool called Logarithm

To some people, logarithm is something quite useless in everyday life. Not so, if you want to visualize the odds of some events. For example, the chance of winning the grand prize in Powerball is one out of 292201338. This is quite hard to comprehend and not so easy to remember. How do we make this number more comprehensible ?

There are many, many ways but the most handy ones are comparing the number of coin flips( when you get only consecutive heads or tails) or the number of dice throws ( when you get an unbroken sequence of just one number ,e.g. 333...333 )which are equivalent to this winning event.

Now, the chance of getting a head in a coin flip is 1/2.

(1/2) ^ x = 1/292201338 ?

Now this is equivalent to the equation:

x * Log2 = Log 292201338

The answer is 28.12 . That means if you are lucky enough to get 28 plus heads (or tails ) in a row in a series of coin flips, you can win a powerball grand prize.

To find out the equivalent number of dice throws in which you get a certain number ( from 1 to 6 ) in an unbroken sequence, we have:

y*Log 6 = Log 292201338

y=10.88( That means you have to get a six ( for example) so many times in succession .)

In Hong Kong, we have the Mark Six Lottery. It is a bit simpler than Powerball. You just pick six numbers out of 49 balls . The chance of getting all six numbers right ( one out of 13983816) is equivalent to 23.73 coin flips and 9.18 dice throws.

cool

To give a further example: what is the chance of landing your fingertip on say, your best friend, in a photo with 200 people when you are blindfold and there isn't a lot of spare space on the photo ?  The chance is 2.95 dice throws or 7.64 coin flips.

One further example: What is the odds of just "spelling out" the numbers that fill a sudoku column ( or row ) with only blind guess and ending up with the correct answer ?  It is one out of 9! ( nine factorial )= 1/362880

It is equivalent to 7.14 dice throws or 18.47 coin flips.