Math odds question

[Rome]

I have no idea.  I suck at math and just did what Sassy did (13 X 10 X 10 = 1,300). 

[phattymatty]

nah, the chances of getting pocket aces just once are 220 to 1.  (52/4) x (51/3)

so i guess 3 times in a row would be 220 x 220 x 220?

[thrillhouse]

Well you dont know anyone elses cards, so you can count that.

The first time around you have a 4/52 chance of getting and ace.  The second time a 3/51 chance.  which equates to a 0.452% chance or about 1/200, of getting two aces.  Your chance of getting that hand three times in a row is like 1 in 9 million.  I wonder if thats right.

Odds of getting hit by lightning 1/600,000
Odds of winning lottery 1/60,000,000

[Susquehanna Birder]

That's about right. I forgot that suit didn't matter, so you're right about 4-52 and 3-51.

If it's only you drawing from the deck (not even the dealer in this example), it's like this:

52/4 = 13
51/3 = 17

Odds of getting 2 aces from the deck with the first two cards drawn: 13 X 17 = 221 to 1.
Doing it 3 times in a row is 221 X 221 X 221, which is 10,793,861 to 1.

[phattymatty]

ok, thats the number i came up with first. 

i should play the lottery.

[Tomahawk]

ok, thats the number i came up with first. 

i should play the lottery.

You'd be a sucker not to.

[Wingspan]

this is actually one hell of a stumper

if there are 4 people at the table, and you are dealt first the odds on ace #1 are 4/52, the second ace would be very complex. you have to factor the 3/51 for player #2, the 3/50 for player #3, and the 3/49 for player #4. your next card is out of a pool of 48 cards.

[PoopyfaceMcGee]

this is actually one hell of a stumper

if there are 4 people at the table, and you are dealt first the odds on ace #1 are 4/52, the second ace would be very complex. you have to factor the 3/51 for player #2, the 3/50 for player #3, and the 3/49 for player #4. your next card is out of a pool of 48 cards.

Right.  There are multiple different scenarios, depending on how many people are at the table... but the 1/221^3 is the simplest way to come to a nearly-correct answer.

[phattymatty]

this is actually one hell of a stumper

if there are 4 people at the table, and you are dealt first the odds on ace #1 are 4/52, the second ace would be very complex. you have to factor the 3/51 for player #2, the 3/50 for player #3, and the 3/49 for player #4. your next card is out of a pool of 48 cards.

i think you're thinking too much into it.  you don't know whether other people get an ace or not, so you don't have to factor them in at all.  whether there are 10 people at the table, or you're just pulling from a deck by yourself, the odds should be the same.

[Cerevant]

i think you're thinking too much into it.  you don't know whether other people get an ace or not, so you don't have to factor them in at all.  whether there are 10 people at the table, or you're just pulling from a deck by yourself, the odds should be the same.

Agree - in a random shuffle the probability of the aces being the first 3 cards is the same as the probability of the ace being every nth card.

[Sgt PSN]

The odds of drawing pocket aces in hold 'em 3 hands in a row are better than the odds of the Flyers and/or Sixers making the playoffs this year. 

[PhillyandBCEagles]

I think the answer to the first one would only be 1/100, because you don't have to get a specific name 3 times in a row; you just have to get whichever one you pick the first time, 2 more times.  So I don't think the odds factor in on the first try, but I could be wrong

[Sgt PSN]

I think the answer to the first one would only be 1/100, because you don't have to get a specific name 3 times in a row; you just have to get whichever one you pick the first time, 2 more times.  So I don't think the odds factor in on the first try, but I could be wrong

Good point.   Looking back at how the question is worded, it seems to suggest randomly picking a name from the hat and then trying to draw it 2 more times rather than picking a predetermined name on 3 consecutive pulls. 

Kudos to you. 

[MURP]

so what the hell is the real answer.  ha. 

[SunMo]

spaghetti