>>>>>>>>>>>"Acting Lottery Director Gardner Gurney said this was only the third time in Lotto’s history that a winner has hit the jackpot twice. The odds of winning just once were 22.5 million to one."
>>>>>>>>>>>
>>>>>>>>>>> ... and a second time, therefore is still 22.5 million : 1, surely. The fact that it's happened twice before is further indicative evidence of this.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>Correct. However, the odds of winning twice are actually much, much smaller. Should be 22.5M * 22.5M to 1. Of course, that's for a single ticket.
>>>>>>>>>
>>>>>>>>>You sure about that? From my memory of stats back in college you have just the same odds EACH TIME, no matter how many times you've already won.
>>>>>>>>>
>>>>>>>>
>>>>>>>>Yes, the odds are the same each time, but to calculate the odds of a particular person winning twice, you multiply the odds of winning the first time by the odds of winning the second time.
>>>>>>>>
>>>>>>>>Let's take a simpler example:
>>>>>>>>
>>>>>>>>You roll one die, looking for a 5. The odds are 1 in 6. Do it again, the odds are again 1 in 6.
>>>>>>>>
>>>>>>>>But what are the odds that rolling the die twice, you'll get two 5's. One in thirty-six, because there's only one combination of the thirty-six combinations that is 5,5.
>>>>>>>
>>>>>>>Sorry, don't understand that explanation at all. I'd've though the chance of getting 2 X 5, in 2 throws, would be 2 in 12, ie 1 in 6 - just the same.
>>>>>>>
>>>>>>>>
>>>>>>>>Now, the lottery thing isn't actually that simple. 22.5M x 22.5M would actually be the chance of winning both of two particular drawings rather than the lifetime chance of winning twice. That's somewhat higher, since each time you play, you have the same chance, but with the odds so small, the repeat plays don't count for much.
>>>>>>>>
>>>>>>>>>And the odds of winning twice with just one ticket are ZERO I'd have thought.
>>>>>>>>>>
>>>>>>>>
>>>>>>>>Well, yeah, I meant one ticket each drawing.
>>>>>>>>
>>>>>>>>Tamar
>>>>>>
>>>>>>I agree with you Terry. The odds don't change just because you've won it before. The odds remain the same through each lottery or throw of the die. The logic that Tamar is trying to apply, though it sounds reasonable is incorrect.
>>>>>
>>>>>
>>>>>Her logic wasn't incorrect but you may be talking about two different things. She was describing the odds of the same thing happening twice. (Not the odds in independent events such as the first and second lotteries).
>>>>
>>>>What, like the odds of winning twice with the same numbers? Maybe, I guess.
>>>
>>>
>>>No, of winning twice, period.
>>>
>>>Does it make sense that the odds of winning twice would be exactly the same as the odds of winning once? (Note that this is NOT the same thing as winning a second time given that you have won once).
>>
>>Yes, afaics, with 2 plays it's the same odds each time. Mind you, each time the odds are astronomical so we don't see too many success stories - only thrice in the lottery history (of how many millions entries?).
>>
>>Take it to its simplest: if you toss a coin, it's 1:2 you'll get a heads.
>>
>>Next toss it's not 1:4 you'll get heads, then for a third 1:16 (1:8 or whatever) - it's still 1:2. By the end of 64 tosses, by that logic, like the old grains of sand on a chessboard conundrum, the chances of getting heads would be practically infinity:1.
>>
>>64 tosses would on average produce 32 heads, so each toss has a 1:2 chance.
>>
>>That's how I see it.
>
>
>You describe the probability of independent events correctly. Once again, though, THAT IS A DIFFERENT QUESTION. (Caps intended). The question was the chances of winning the lottery TWICE.

Suppose you'd won the lottery. The reason why you don't win it again is not cos it's gone from astronomically high odds to tera-astronomically high odds, it's cos it's astronomically high odds each time. Give me several decks of cards my chance of pulling out a King is 1:14 each time. Give me 14 decks and I may pull out 1 K. Give me 28 decks and I may well pull out 2.

This works both ways. They say a rubber fails 1:10 (say). This doesn't mean you thank god for your luck on the 9th use of one then avoid the 10th - the odds don't get closer with each use. Each Johnny has a 1:10 chance of failing.