Holding AQ. What high card has highest prob on flop?

[Openside]

I was talking to spoon on mIRC and was posed this question:
[23:43] <spoonitnow> if you hold AQ
[23:43] <spoonitnow> what's the most likely high card on the flop
01[23:43] <Openside> K
[23:43] <ZwiFTiBAF> buuuuurt
[23:43] <ZwiFTiBAF> wrong
[23:44] <spoonitnow> an ace is still the most likely high card
[23:44] <spoonitnow> isn't that sick


[23:50] <spoonitnow> chance of an a-high flop if we take an a and a q out of the deck is like (3/50)*(47/49)*(46/48)*3
[23:51] <spoonitnow> ok so chance of a k-high flop under the same circumstances is
[23:52] <spoonitnow> actually that's wrong
[23:52] <spoonitnow> it should be
[23:52] <spoonitnow> (3/50)*3, i think
[23:52] <spoonitnow> anyway
[23:52] <spoonitnow> so here comes the K-high flop train
[23:53] <spoonitnow> (4/50)*(46/49)*(45/48)*3 = 0.21
[23:53] <spoonitnow> which should be lower than (3/50)*3 = 0.18

I like to figure things out for myself and hate it when i can't. I am missing something, I cant figure why A has the highest prob.
Here is my logic: we hold AQ
Flop can come Axx, xAx or xxA
Prob. of hitting at least one A on flop = 3/50+3/49+3/48 = 0.18


Now prob of the flop hitting a K and no A is
K, no A, noA + no A, K, no A + no A, no A, K
= (4/50*46/49*45/48)+(47/50*4/49*45/48)+(47/50*46/49*4/48) = 0.21

So to me hitting a K and no A is higher prob. than hitting an A on flop.

Damn it, where am i going wrong?

[celtic123]

I might be barking up the wrong tree, but It it like a trick question?

Maybe its not to do with maths.

I was talking to spoon on mIRC and was posed this question:
[23:43] <spoonitnow> if you hold AQ
[23:43] <spoonitnow> what's the most likely high card on the flop

I dont see how the K can be the most likely High card, because the J is equally most likely and this is also a high card.

Its like saying , higher cards have more chance than low cards of landing in the flop.

[Openside]

I might be barking up the wrong tree, but It it like a trick question?

Maybe its not to do with maths.





I dont see how the K can be the most likely High card, because the J is equally most likely and this is also a high card.

Its like saying , higher cards have more chance than low cards of landing in the flop.

No i dont think its a trick question. Think of it as "which has a higher prob. of hitting the flop A or K and being high card?"

[celtic123]

Think of it as "which has a higher prob. of hitting the flop A or K and being high card?"

[Imthenewfish]

Now prob of the flop hitting a K and no A is
K, no A, noA + no A, K, no A + no A, no A, K
= (4/50*46/49*45/48)+(47/50*4/49*45/48)+(47/50*46/49*4/48) = 0.21

So to me hitting a K and no A is higher prob. than hitting an A on flop.

Damn it, where am i going wrong?

Why does it matter what order they're in? Just find the probability of a king flopping and then subtract it by the probability of an ace hitting the other two cards. (4/50+4/49+4/48)-[(3/49)+(3/48)]?(0.8+0.816+0.833)-[(0.0612)+(0.0625)=24.5%-12.37%
probability of a king being the high card should be something like 12%

[spoonitnow]

There are K-high flops and there are A-high flops. Which is most likely if you hold AQ?

[spoonitnow]

Btw I f'ed up the original question, K-high flops are the most likely in that scenario. Meant to ask if we hold AK which is most likely, an A-high flop or Q-high flop.

If we hold AQ then A/K-high flops are of similar likelihood.