Test Your Instinct

Bozzer

You hold AQ UTG in a 10-handed game. What percentage of the time will someone behind you hold AA/KK/QQ/AK?

Post your 1st instinct answer,ie don’t post if you’ve thought about it too long or done the math.

Not very exciting, just curious to see how close the guesses are.

De Deraco

5% first guess

Doc Farrell

i know this one!

its either never

or

always, especially if ur on the bubble!

so roughly 14%

Shortstack

Around 24.67%

kincsem

2.3%

Shortstack

My first guess was for everyone else. For me it is 200%, usually there will be at least two of those hands

Davey Devil

0.176%

The Troll

i'd say 10%

RoundTower

a million to one.

Imposter

Which site are we on or who's the dealer if it's live?

Spiritus

Imposter wrote:

Which site are we on or who's the dealer if it's live?

Good man. Straight to the heart of the problem

Doc Farrell

jaysus man,
post the answer.
i'm right anyway , its about 12-14 %

Ste05

OK, I'd guess about 6.7%......

jtsuited

14.8%

Bozzer

ok Doc...the answer is about 17%.

Here's a way to do a rough calculation at the table if you're
into that sort of thing....

Everyone should know the chances of somebody being dealt a pair of aces(or any specific pair) are 1/221. This takes into account the 6 different ways you can be dealt aces.

But the odds are half this(0.5/221) for aces and queens as we hold AQ, leaving only 3 combinations.

The odds remain the same though for kings.

There are twelve ways of being dealt AK which is twice as many as for kings
and so the odds are 2/221.

There are nine players behind you so you can approximate to

9/221*(0.5 + 1 + 0.5 + 2) = 36/221 = 16%
9/221*(AA + KK + QQ +AK)

Another method

You hold AQ, leaving 50 cards.
Total remaining 2-card combinations are 50*49/2=1225.
Total ways to hold AA/KK/QQ/AK (given your AQ) =24.
24 is nearly 2% of 1225.
So, the odds of one opponent NOT holding one of those hands is about 98%. The odds of 9 opponents NOT holding is (.98)^9 = 0.833

So the chances somebody holds one of these hands is 1-0.833 =16.7%

It's unlikely you'd be able to do this one in your head tho

jtsuited

i was so close. i was so close. yes yes yes. i like quizzes. more of the same, i say

kincsem

My guess of 2.3% was based 4 hands from 169 possible = 4/169 ~ 1/40 or just less than 2.5%.

I forgot there were nine f****** behind you.

So 9 X 2.3% = 20.7% but you hold AQ which lessens the %

kincsem

Combinations are 6 + 6 + 6 + 6 = 24
Holding AQ reduces this to 6 + 3 + 6 + 3 = 18

Or 20.7% X 18/24 = ~ 15.5%

bmc

kincsem wrote:

My guess of 2.3% was based 4 hands from 169 possible = 4/169 ~ 1/40 or just less than 2.5%.

I forgot there were nine f****** behind you.

So 9 X 2.3% = 20.7% but you hold AQ which lessens the %

the 169 possible hands don't have equal probabilities.

Also...

kincesm wrote:

So 9 X 2.3% = 20.7%

Probability doesn't work like that...

I'm too lazy to calculate though so maybe I should just get back in my box...

geoid

I think that's correct with 24 combinations of AA KK QQ AK

ie.

AAA (3 aces left)
KKKK (4 kings left)
QQQ (3 queens left)

To make all AA combinations that would be 3
To make all KK combinations that would be 6
To make all QQ combinations that would be 3
To make all AK combinations that would be 12 (for each A you combine it with 4 kings 3*4=12)

Add them up and you get 24 possible combinations of AA, KK, QQ, AK

Hitman Actual

kincsem wrote:

My guess of 2.3% was based 4 hands from 169 possible

There are 1326 possible starting hands in holdem (52C2), not 169. I think the 169 number comes from Sklansky's groupings.

hotspur

Want to scare yourself away from ever playing online poker again????
On pokerstars they have some nonsense $5 quadruple shootout tournament, but for some reason they replay the final table a week later...with all of the hands face up from the beginning. I was watching it for a while yesterday or the day before, and Jesus it was scary the hands that were out there consistently with only 6 players when I tuned in. Now obviously the players were no world beaters but it was quite interesting to watch, look out for it some time if you need to scare yourself tight!