Which Lottery Statement Is Correct: Equal or Biased Probabilities?


Last updated on June 6, 2024

Hi Edvin,

I see claims being made that contradict each other. Your reply to this one question will answer all my other questions.

All combinations in the lottery have an equal probability of getting drawn.

Combinations are not created equally.

Since both statements can not be true simultaneously, which statement are you claiming is true?


Hi David,

Thank you for your writing in. Let me shed some light on your question.

  1. All combinations have the same probability.1 That will not change. It’s a mathematical fact.
  2. Although combinations have the same probability, they don’t have the same composition. Since combinations have different compositions, we separate them into combinatorial groups2 with varying success-to-failure ratios. Therefore, we use combinatorial groups to extract useful mathematical information to help lottery players make informed decisions. In lotterycodex, we present this information as the S/F ratio.

To give you some background, odds and probability are two different terms in mathematics. They have different equations.3

Probability = A/B

Odds = A/(B – A)


A = number of favorable events.
B = all possible combinations

Now, since all combinations have the same probability, you may think it is OK to play 2-4-6-8-10-12 or 10-20-30-40-50.

But your gut feeling tells you, “Those combinations are not the most sensible choices you can make as a lotto player.

You must understand the difference between odds and probability to support your gut feeling. You cannot manipulate probability, but you can make an intelligent decision.

How do you make that intelligent decision? You choose better odds that are more favorable to you. 

Therefore, the most sensible strategy relies on choosing a better success-to-failure ratio rather than focusing on the probability of individual combinations. This is how you make informed choices when playing a lottery game.

I hope that helps.

Stay safe,

Additional Resources

  1. Probability course    []
  2. Introduction to Combinatorics    []
  3. The Difference Between “Probability” and “Odds”    []

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