… of same six winning numbers , **twice in a row** , in Bulgaria’s national lottery was a freak coincidence, officials said Thursday.

Story here.

… of same six winning numbers , **twice in a row** , in Bulgaria’s national lottery was a freak coincidence, officials said Thursday.

Story here.

Without going into the details (such as “6 out of *how many* numbers?”) – and taking the quoted probability of 1:4,000,000 – it would be interesting to ask these questions:

- How many draws of 6-number lotteries have occurred,
**ever**, in repeating (i.e., daily or weekely) lotteries, around the world? - If (as I suspect) this number is in fact in the neighborhood of “millions,” has any such case (of repeating draws) ever been documented before?
- If (as I suspect) the answer to Q2 is “no,” then why are we surprised that an event that is statistically “due” actually happens?

All of this of course hinges on the assumption that the Bulgarian lottery, and Bulgarian officials in general, can be trusted (that is, “Assume a *fair* die…” as posited in most probability questions of this ilk :D) – But I really don’t see how this occurrence is truly “unbelievably unlikely,” given the vast number of lottery draws over a number of decades, week after week and sometimes more often than that.

I figured out that the odds of winning the Mega Millions game in Washington are 175,711,535 to 1.

How many numbers to choose, out of how many possible?

It looks like the Bulgarian Lotto is 6 / 42 (look for “bulgarian” on the page,) which I calculate as giving a chance of winning of 42!/6!*36!) or a bit worse than 1:5,000,000 – which should be exactly the same chance as a repeat draw (consider “winning” to be “the actual draw duplicating your.”) TheGreenRoom seems to agree with me on the odds…

So – not at all beyond belief, again, assuming we trust those guys!

MegaMillions and Powerball are much lower odds than a standard lottery because of the sixth ball and number of balls.

Powerball odds (from their website)

POWERBALL® PRIZES & ODDS

Ticket Cost $1

5 of 5 + PB Jackpot 1:195,249,054.00

5 of 5 $200,000 1:5,138,133.00

4 of 5 + PB $10,000 1:723,144.64

4 of 5 $100 1:19,030.12

3 of 5 + PB 1:13,644.24

MegaMillions odds (from their website)

5 of 5 + 1 Jackpot 1:175,711,536

5 of 5 $250,000 1:3,904,701

4 of 5 + 1 $10,000 1:689,065

4 of 5 $150 1:15,313

3 of 5 + 1 $140 1:13,781

So, your snowball’s chance in hell is marginally better with MegaMillions vs Powerball. And I’m thinking if the Bulgarian lotto is only 1:4,000,000 odds then they’re using a much lower number range on 6 numbers.

Five numbers are chosen from a field of 56 and one number is chosen from a field of 46.

So the probabilities are 1/3,819,816 and 1/46, and the probability of winning the jackpot is 1/175,711,536 (or 175,711,535:1).

I’m pretty convinced that 1:4,000,000 is wrong, and it’s more like 1:5,250,000 – but yes, they only use 42 numbers to draw from.

This has happened before - sort of.

When I was living in Germany, one lottery draw had something insane like 245 winners!

Lottery officials were scratching their heads, unable to figure out how so many people picked the exact same winning numbers!?

The answer?

The lottery numbers in Holland were drawn on Friday, and the numbers in Germany were drawn on Saturday. It seems that a lot of people on the border of Germany/Holland would watch Dutch television, get the Dutch winning numbers and then play them in the German lottery the next day. Sure enough - that week the numbers in Germany were indeed the same as those numbers in Holland!

The good news for them? It worked, and they won!

The bad news for them? They weren’t the only one, and by the time the pot was split, they all got about enough to maybe buy a new car.

(Some had quit their jobs when they found out they won, others were trying to decide which villa to purchase - the dreams all went “poof” when the final tally of winners was announced. Rule number one: Wait until the money is in your hand before you make any rash decisions!)

“Sergei, you idiot - those were the numbers we used to fix last week’s drawing…”