Woman hits "trillion to one" shot

[SomethingClever]

link (http://www.local6.com/news/4468309/detail.html)

Well, still just a million to one, or whatever. But the fact that she hit it twice is impressive.

[closer2313]

She would have to hit it twice in a row and have only played it twice for it to be a trillion to one shot.

[nanoCRUSHER]

This wasn't a dollar slot, it was a penny slot.

[BlueBear]

Looks like I my strategy wrong all along, like her, I should have stuck to the same machine!

[etgryphon]

Not really. If winning the jackpot was an independent event, then she would have to play it just twice with any length of time between the two events.

That maybe what you are saying I just want to clarify.

Example: odds of winning jackpot 1:1,000,000

Situation A:

Woman pulls lever for the first time, wins the jack pot (Event A). The woman pulls it the second time and wins the jackpot (Event B)

odds of Event A * odds of Event B = 1:1,000,000 * 1:1,000,000 = 1:1,000,000,000,000

Situation 2: Woman pulls the lever for the first time(Event A) and wins jackpot. Takes her money home. 10 years later, She pulls the lever on the jackpot for the second time and wins (Event B).

odds of Event A * odds of Event B = 1:1,000,000 * 1:1,000,000 = 1:1,000,000,000,000

Still the same odds, but spanned over 10 years. There is no time element only the event elements.

-Gryph

[LetYouDown]

So I've had pocket Aces 1000 times since I started playing poker. The odds of getting A-A preflop is 1/221. Granted, I've played hundreds of thousands of hands...but that's irrelevant?

Sweet, I hit a 1-in-2.4675938837065992401101191361579e+2344 longshot! I'm not following. Obviously time isn't a factor, only number of hands. I think it's pretty safe to say that she didn't only pull the lever twice in 10 years.

[etgryphon]

[ QUOTE ]
So I've had pocket Aces 1000 times since I started playing poker. The odds of getting A-A preflop is 1/221. Granted, I've played hundreds of thousands of hands...but that's irrelevant?

Sweet, I hit a 1-in-2.4675938837065992401101191361579e+2344 longshot! I'm not following.

[/ QUOTE ]

No. Sorry to disappoint you.

You have played many more hands than the 1000 hands that you got AA. I'm just saying your odds are based off of the sample size and consecutivity(sp?) without a time element.

So in your case, if you sat down at a table and play exactly one hand of holdem and got AA (Event A). Got up from the table and left for a week while people played poker with the same deck, changed the deck, played 1000s of hands. Then you came back and sat down played exactly one hand and got AA (Event B).

For you, the odds of that happening would be:

((# of ordered events) * Odds of Event A) * ((# of ordered events) * (Odds of Event B)) = ((1) * (1:216)) * ((1) * 1:216) = 1:46656

Now lets take the case of where you sit down and play 10 hands each time and one of those hands you get AA.

So now you have events 1 - 10 in the first session
and events 11 - 20 in the second session.

Session #1:
9 events where you DID NOT get AA: odds = 215:216
1 events where you DID get AA: odds = 1:216

Odds of Session #1:
(10) * ( (1/216) * (215/216)^9 ) = 1:~21.5

Session #2:
9 events where you DID NOT get AA: odds = 215:216
1 events where you DID get AA: odds = 1:216

Odds of Session #2:
(10) * ( (1/216) * (215/216)^9 ) = 1:~21.5

So odds of Session #1 and Session #2 happening:

1 * (1:21.5)^2 = 1:463.16

Hope this is clear. Mistakes?

-Gryph

[closer2313]

If you play 2 hands, what are the chances of getting AA back to back?

If you play 300 hands, what are the changes of getting AA back to back?

[etgryphon]

[ QUOTE ]
If you play 2 hands, what are the chances of getting AA back to back?


[/ QUOTE ]

(1:216 * 1:216) = 1:46656

[ QUOTE ]

If you play 300 hands, what are the changes of getting AA back to back?

[/ QUOTE ]

At least once? Well, you can break it up to 150 mini-sessions of two hands each.

150 * 1:46656 = 1:310.1

I think....

-Gryph

[LetYouDown]

[ QUOTE ]
Hope this is clear. Mistakes?

[/ QUOTE ]
Sorry, apparently my attempts at sarcasm don't go over well early in the morning. Didn't mean for you to have to reiterate trivial math.

[etgryphon]

[ QUOTE ]
[ QUOTE ]
Hope this is clear. Mistakes?

[/ QUOTE ]
Sorry, apparently my attempts at sarcasm don't go over well early in the morning. Didn't mean for you to have to reiterate trivial math.

[/ QUOTE ]

LOL,

When I was typing up the whole thing I was saying to myself, "LetYouDown, knows this stuff..."

I'm an idiot. It was fun to do though.

-Gryph

[closer2313]

I think im very confused on who is replying to what. Who introduced a time element into the question? I don't think it was me. I said she would have to win it twice in a row and have only played it twice for it to be a trillion to one.

I didn't mean by in a row, as in 2 seconds apart, just no other pulls of a lever in between.

well, what I was asking is, she would only have to play the slot twice and win both times for it to be a trillion to one shot right?

If she played the slot 10,000 times, then it is much more likely to win the jackpot twice correct?

Also with AA twice over 300 hands, isn't there 298 ways to play 2 hands in a row?
IE. for 10 hands, 12 , 23, 34, 45, 56, 67, 78, 89, 910 is 9 ways to play 2 hands in a row, so for 300 hands it would be 298.

Chance of getting AA twice in a row would be 298 * 1/221 * 1/221.

That was my argument against a trillion to one shot. Should we have to have played it only twice and won both times so it would be like this 1/1,000,000 * 1/1,000,000 not, I played it 10,000 times and won twice. 10,000 * 1/1,000,000 * 1/1,000,000. I just had a problem thinking that she only played the slots twice and won both times creating a true one to a trillion shot. I would have to think she played and played and played and won twice, and that it was no where near a trillion to one shot.

where am I wrong?

[etgryphon]

[ QUOTE ]
well, what I was asking is, she would only have to play the slot twice and win both times for it to be a trillion to one shot right?

If she played the slot 10,000 times, then it is much more likely to win the jackpot twice correct?

[/ QUOTE ]

Yes. I made a mountain out of a mole hill.

-Gryph

[closer2313]

I edited my post, I was wondering if you could look at it and tell me if my thinking is correct.

I don't get to take a probability course till my third year of college, so I'm trying to teach myself how to do it, so any clarification would be extremely helpful.

Thanks.

[etgryphon]

[ QUOTE ]
I edited my post, I was wondering if you could look at it and tell me if my thinking is correct.

I don't get to take a probability course till my third year of college, so I'm trying to teach myself how to do it, so any clarification would be extremely helpful.

Thanks.

[/ QUOTE ]

Its right on. My whole post was on the fact that there is no time element. Someone might have read your post and think that she had to play it back to back without someone playing it between the two times that she played.

But, like Let said this is a trivial point that I blew out of proportion.

BTW: I never took a statistics class. I'm doing the same thing that you are doing. I'm just pretty fond of math.

-Gryph

[LetYouDown]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Hope this is clear. Mistakes?

[/ QUOTE ]
Sorry, apparently my attempts at sarcasm don't go over well early in the morning. Didn't mean for you to have to reiterate trivial math.

[/ QUOTE ]
Hehe. My apologies. I replied merely because I wanted to figure out the odds of having A-A a thousand times in row. Not overly likely.

I was inspired by office commentary this morning from a woman who said "I can't believe that guy who won $800,000+ at the Kentucky Derby bet a 50-to-1 longshot." She believed that he only bet one horse and got paid that much. I tried to explain the number of permutations for the top 4 horses in a 20 horse field. I gave up after roughly 45 seconds when it was apparent I was talking to a brick wall.

LOL,

When I was typing up the whole thing I was saying to myself, "LetYouDown, knows this stuff..."

I'm an idiot. It was fun to do though.

-Gryph

[/ QUOTE ]