A/K vs QQ

[Legend27]

What is the % chance of A/K matching either the A or K on the turn and river? I don't wanna know if it's 6:1 odds or whatever, I just wanna if it's like a 20% chance or whatever it is.

[Jimbo]

About a 27% chance. Actually I always thought that was why you used your nickname of Legend27, guess I was wrong. [img]/forums/images/icons/smile.gif[/img]

[Legend27]

27 is just my lucky #. Thanks for replying.

[Cyrus]

"I don't wanna know if it's 6:1 odds or whatever, I just wanna if it's like a 20% chance or whatever it is."

IMHO, knowing how to convert odds to percentages and vice versa, rather quickly too, is more important than knowing my chances to hit. I mean, I should learn to do the first and then move on to know the other stuff. JMHO.

Odds of 6:1 against is equivalent to hitting (1/7)% of the time, ie 1/7=0.14 or 14%. The probability of hitting 20% of the time is equivalent to having 80%-20% odds against, which is being a 8:2 or 4:1 underdog.

"What is the % chance of A/K matching either the A or K on the turn and river?"

With 6 outs (3K+3A), the probability of hitting the turn and/or the river is around 24%.

This does NOT mean that your AK will win over QQ abt 24% of the time in that situation ! One of the two cards to come might be an Ace (or a King) but the other card a Queen. Ouch.

Here's the table with the probabilities of hitting your outs, when you have the turn and the river coming up:

<pre><font class="small">code:</font><hr>

TURN AND RIVER COMING UP


NUMBER OF PROBABILITY OF HITTING
OUTS ONE OR TWO OUTS

1 4.3 %
2 8.4 %
3 12.5 %
4 16.5 %
5 20.4 %
6 24.1 %
7 27.8 %
8 31.5 %
9 35.0 %
10 38.4 %
11 41.7 %
12 45.0 %
13 48.1 %
14 51.2 %
15 54.1 %
16 57.0 %
17 59.8 %
18 62.4 %
19 65.0 %
20 67.5 %
21 69.9 %

</pre><hr>

[Legend27]

n/m

[Cyrus]

Here's how the probabilities in the Table posted above were calculated. Take, for example, the probability of having 6 outs and hitting 1 or 2 outs on the Turn and the River.

C(6,2)=15 is the number of 2-card combinations that those 6 outs can produce. That means there are 15 combinations of Turn+River whereby you hit your outs in both cards.

For the number of hitting only 1 out (and get 1 blank), you have 6 outs and (52 - 2cards in your hand - 3cards on the flop -6 outs)= 41 blanks. Combining the outs with the blanks gives you 6*41=246 combinations whereby you hit only 1 out on Turn+River.

So, we have 15+246=261 combinations producing either 1 or 2 outs on Turn+River.

The total combinations of all the remaining cards that can be seen on Turn+River are
C(47,2)=1081.

Therefore, the probability of getting a combination of Turn+River that hits you with 1 or 2 outs is 261/1081=0.241443108233117483811285846438483 or 24.1%.

[It is irrelevant in this calculation whether you hit your 1 out on the Turn or on the River. The probability of hitting 1 out in either Turn or River is the same, before the Turn card is dealt.]

[Jimbo]

Cyrus thanks for confirming that my about 27% was correct and your 24.1% did not take into account the fact that you knew the other player holds QQ.

[Cyrus]

The original question seemed clear enough to me ("What is the % chance of A/K matching either the A or K on the turn and river?"). The poster however had "A/K vs QQ" in his post's title. So, I guess, this could be interpreted two ways : We want the chance of hitting our AK (1) not knowing our opponent holds QQ, and (2) knowing our opponent holds QQ.

The probability for the first case, where we don't know anything actually about our opponent's hand, was provided above, and is 24.1%. The whole Table in the "Addendum" post, in fact, is based on ignoring what our opponent holds. Which is the usual situation at the tables.

The probability for the second case is indeed higher than the first, because we know that our opponent holds QQ which means he holds neither Ace nor King! The probability, of our AK hitting the Turn and/or the River, is actually the same whether our opponent holds QQ or J5. No matter what he holds, as long as he doesn't have A or K.

Thanks to Jimbo for helping me clarifying this.

--Cyrus

PS : AK is of course a dog against QQ in the situation we examine, i.e. when neither has hit the flop. With a raggedy flop that helps neither hand, e.g. 9 6 3 rainbow, QQ is a 3.2:1 favorite against AKo, and 2.5:1 against AKs.

[Legend27]

Let me start my reply off by saying i'm not good at math.

So if you have a 24% of matching the A or K on the turn and river then lets say we saw the turn and it was not an A or K then on the river A/K would have 6 outs and about a 12% of matching?

So if A/K has a 12% of matching on the river, wouldn't that mean A/K has a little less than a 60% chance of matching the A or K after 5 cards were dealt? (5 x 12%)
I know that that is not right, I just want to know why my thinking is flawed.

Here's a random question: You hold A/Ks. You are not playing against an opponet. What % of the time does A/Ks match the A or K, get the straight, or get the flush? What I mean is what is that total %?

[Cyrus]

"I'm not good at math."

That makes two of us. Everybody else here is very good.

"If you have a 24% [chance] of matching the A or K on the turn and river then let's say we saw the turn and it was not an A or K, then on the river A/K would have 6 outs and about a 12% of matching?"

Don't divide that 24.1% in half! Here's the correct (and quite straightforward) calculation : You have 6 outs and 1 card to come. (52 - 2cards in your hand - 4cards on the board)=46 unseen cards, and 6 outs. 6/46=0.13 or 13%.

(This assumes that you don't know what your opponent holds or doesn't hold.)

"So if A/K has a 12% of matching on the river, wouldn't that mean A/K has a little less than a 60% chance of matching the A or K after 5 cards were dealt? (5 x 12%)"

I'm sorry but I don't know what you mean. Are you perhaps saying that, with "5 cards to be dealt", the chance of hitting your AK is 60%? It's not. You shouldn't multiply the number of cards to come with the probability of hitting with one card to come!