what would the odds be....

[myonker]

Can someone please help me out with this. I'm a horrible Math person

Suppose I have K-10off, in a 10 player, and the flop comes AAK. What are the odds of someone holding an A?

Ive seen some things such as:

5 Players, there's an A on the flop. Chances a player has an A in their hole are 1.7 : 1

But how are these odds figured out???

I'm sure this is a dumb question, but I'm dumb so thats that

Thanks in advance!

[american mutt]

ok,,
52 cards, 20 are hole cards, 3 burn cards, so of the 18 cards
that matter, the other players holes, the chances of one or more
of them holding an ace is ... 18 of ....52-7, table and your hole,
45-3, the burns, 18 of 42, 2 aces left in the deck,, 42/18 = 2.3333
2 o/o 52 = 26, so 26/2.3333 = 11.1 so, 11.1 to 1
ok, I need to read up on this, I'd say the odds are good.
I tried to freelance it, my math is bad too.

[FatJoe]

dont forget that people are more likely to play an ace than any other card. so among people seeing a flop an ace is the most likely card for them to have. it's not a clear-cut math problem.

[Adamm]

If everyone played their hand regardless of what they held the odds would be...
10 players, you have KTo, flop is AAK.
2 Aces left in the deck, 47 unseen cards. 18 of those unseen cards are held by other players.
Chance that the 18 other cards are not an ace would be:
(45/47)(44/46)(43/45)(42/44)(41/43 )
(40/42)(39/41)(38/40)(37/39)(36/38 )
(35/37)(34/36)(33/35)(32/34)(31/33 )
(30/32)(29/31)(28/30)

which is the same as:
(45x44x43x42x41x40x39x38x37x36x35x34x33x32x31x30x29x28) /
(47x46x45x44x43x42x41x40x39x38x37x36x35x34x33x32x31x30)

which is the same as:
(29x28)/
(47x46)

and that's equal to:
0.37557816836262719703977798334875

So 1-that would be the chance that one or more of those cards are an ace:
0.624421831637372802960222016652

Plug that into the odds conversion formula:
1/[(1/p)-1]=x

and get:
1.6625615763546798029556650246374
and round to 1.7