The Principle of Independent Trials: Do 'Hot Numbers' and 'Cold Numbers' Really Exist in Lottery?

“Haven’t the numbers that haven’t appeared in the last 10 draws due to come out soon?” or “I should avoid last week’s numbers” — you’ve probably thought something like this at least once. Let me start with the conclusion: these thoughts are statistically meaningless. This is because each lottery draw is a ‘completely new game.‘

Coin Flipping and Lottery: Understanding Independent Trials

An independent trial refers to a phenomenon where previous results have no influence whatsoever on the next result. The easiest example is coin flipping.

If heads comes up 5 times in a row, does that make tails more likely on the sixth flip? No. The sixth coin flip is still a completely new game with a 50% chance of heads and 50% chance of tails. The coin doesn’t ‘remember’ what face came up before.

The lottery works the same way. In the drawing machine, 45 balls are reshuffled under fair conditions every time. Just because ball number 1 came out last week doesn’t change the probability of ball number 1 coming out this week. It’s still just one out of 45.

The Common Trap of ‘Gambler’s Fallacy’

The ‘Gambler’s Fallacy’ is a psychological trap many people fall into. It’s the tendency to believe that if a particular result hasn’t occurred for a long time, “it’s due to happen soon,” or if a particular result occurs frequently, “it won’t happen for a while.”

• Cold Numbers: Numbers that haven’t appeared as winning numbers for a long time. People expect these numbers to appear soon. (Fallacy!)
• Hot Numbers: Numbers that have frequently appeared as winning numbers recently. People believe this ‘trend’ will continue. (Fallacy!)

Analysis of data from draws 1 to 1,000 released by Donghaeng Lottery shows that the difference in occurrence frequency between the most and least frequent numbers falls within the statistical margin of error. This means that in the long run, all numbers appear roughly the same number of times, proving there’s no tendency for certain numbers to appear more or less frequently.

Is Data Analysis Really Meaningless?

While analyzing past data can’t increase your winning ‘probability,’ it can be referenced for strategies to increase ‘expected winnings.‘

Winning Probability vs. Expected Winnings

• Winning Probability: The mathematical probability of winning first prize. Fixed at 1 in 8,145,060 and absolutely never changes regardless of which numbers you choose.
• Expected Winnings: The expected value of the amount you can receive when you win. If you’re the only one with the winning numbers, you get the entire first prize, but if 100 people have the same numbers, you split it 100 ways.

In other words, avoiding ‘popular number’ combinations that many people choose can be a smart strategy. Past data analysis can be used as reference material to avoid these ‘numbers where people crowd’ — for example, avoiding patterns like marking a vertical line on the ticket or using only birthday-related numbers (1-31).

Conclusion: Enjoying Lottery Wisely

Efforts to predict ‘numbers that will come out’ based on past data are statistically meaningless and risk falling into the ‘gambler’s fallacy.’ Every number has an equal 1/45 chance of being drawn each week.

The true lottery strategy isn’t magic that increases winning probability, but rather selecting ‘your own numbers’ so that if luck strikes, you can receive as much of the prize money as possible. Use past data only as reference material to find ‘numbers to avoid,’ and maintain the attitude of treating lottery as healthy entertainment enjoyed with small amounts.