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Probability Scale: From Coin Flip to Jackpot

One ruler for chances, from a coin flip to a lottery jackpot. Each mark is a real chance from pure math or official game conditions. Drag the ruler above to compare two events.

Loading the simulator

Woman sliding a clip along a long wooden ruler

How to read the ruler

  1. Start at the leftThe most common marks sit at the left end. A coin flip is 1 in 2.
  2. Move one step rightEach step to the right means the event is ten times rarer than one step before.
  3. Count the steps between marksMore steps between two marks means a bigger gap in rarity. Drag the ruler above to compare any two events.
  4. End at the jackpotsLottery jackpots sit at the far right, past every coin, dice and card mark.

Marks on the ruler

EventChanceWhere the number comes from
Coin flip lands heads1 in 2Pure math
One die shows a six1 in 6Pure math
Two dice show double six1 in 36Pure math
Drawing the ace of spades from a deck1 in 52Pure math
Daily Keno, all ten picks match1 in 2,147,181OLG game conditions
Daily Grand top prize1 in 13,348,188Official game conditions
Lotto 6/49 jackpot1 in 13,983,816Official game conditions
Lotto Max jackpot1 in 33,446,140Official game conditions

Lotto Max odds are per play; one play has four selections. More examples: things more likely than the jackpot.

Normal ruler vs log ruler

Normal ruler

  • Equal gaps mean equal differences in chance.
  • A coin flip sits halfway along the line.
  • All lottery jackpots crowd into one dot near zero.
  • Keno and Lotto Max look the same.

Log ruler

  • Equal gaps mean the same ratio of chances.
  • Each step to the right is ten times rarer.
  • Every mark gets its own visible place.
  • Lotto Max sits clearly to the right of keno.

Turning odds into a chance

chance = one ÷ N, when the odds are written as one in N

Example: For example, a die roll is 1 in 6: one face out of all faces. The odds converter shows percent and per million.

Words on this page

Probability
How likely an event is, from impossible to certain. This page writes it as one in N.
Odds of one in N
On average, the event happens once for every N tries. A bigger N means a rarer event.
Log scale
A ruler where each equal step multiplies the rarity by the same amount, here by ten.
Per play
The chance for one paid play of a game, as printed in its game conditions.

Sources

Questions

What is a probability scale?

A line that places events by how likely they are. Common events sit at the left, rare ones at the right. Here the marks run from a coin flip at 1 in 2 to the Lotto Max jackpot at 1 in 33,446,140.

Why use a log scale for odds?

On a normal line, every lottery jackpot sits in one dot near zero. On a log scale, each step is ten times rarer, so keno, Daily Grand, Lotto 6/49 and Lotto Max each get a separate place.

Where does keno sit on the probability scale?

In Daily Keno, matching all ten picked numbers is 1 in 2,147,181. That is far rarer than any card or dice mark, but less rare than the Daily Grand top prize at 1 in 13,348,188 and both jackpots.

How rare is the Lotto Max jackpot on the odds scale?

It is the rarest mark on this page: 1 in 33,446,140 per play. See how big that number looks for a picture of it.

Do quick pick numbers sit at a different spot on the scale?

No. Every combination has the same chance, so quick pick and your own numbers have the same odds. Past draws do not change the next draw.