ITH Poker Forum

[joeblack]

How is everyone. I just joined this site hoping to get a better grasp on the math side of poker. I purchased a copy of "Texas Hold'em Odds and Pobabilities". The book seems to have a lot of good information and I am enjoying studying it. I have a question from the book and am really hoping someone can help me out. Ok, the problem is this:

Floping one pair or better holding A,K

44/50 * 43/49 * 42/48 = 67.6% - 100% = 32.4%

Now I understand that by calculating the probability of it not happening, just subtract and get the probability of it happening. But i'm missing something. Why doesn't this work.

1 out of 3 As or 3 Ks hits then whatever card hits after that dosen't matter.

6/50 * 49/49 * 48/48 = 12% * 3 = 36%

I guess my question(s) are: What am I not seeing and
Is there a rule as to when you know that you should calculate the odds of something not happening and then subtracting from 1 or 100%.

I know these are probably really dumd questions whith really simple answers but I just can't seem to get it.
Thanks in advance to any help.

[leofric]

Firstly hi and apologies for not answering earlier..........

I'm not sure with the second calculation what you're trying to prove.

The odds of hitting an A or K on the first card are indeed 6/50 - then we move into slightly different maths on hitting the remaining cards depending on whether we hit or not first time.

Hence 6/50 * 5/49 on hitting if we did
44/50 * 6/49 if we didnt

If you expand this for the third card you end up with a variety of scenarios all dependant on what happened previously. It's easier to calculate the odds on all 3 missing and subtract from 100 which is why us simple folk do it!

6/50 * 5/49* 4/48
6/50 * 44/49 * 4/48
6/50 * 44/49 * 44/48
44/50 * 6/49 * 5/48
44/50 * 6/49 * 43/48
44/50 * 43/49 * 6/48

In theory that lot should add up to 32.4%!

*Edit - erm I might have deliberately missed the following.....

6/50 * 5/49 * 44/48

but only to show how hard it is!

[jeffnc]

Is there a rule as to when you know that you should calculate the odds of something not happening and then subtracting from 1 or 100%.

The only "rule" I know is that you should do it when it's easier. If the other calculation is too tedious or complicated, then try this one.

For example, what is the probablility of not flipping 3 heads in a row?

Well, first you'd have to add up all the combinations of that.
TTT
TTH
THT
HTT
THH
HTH
HHT
That's (1/2 * 1/2 * 1/2) * 7 = 7/8

That was a pretty simple one, but you could imagine if the probably of each event were different (not all 1/2), or if there were many coin flips.

Now compare that with the probability of flipping 3 heads in a row
HHH
1/2 * 1/2 * 1/2 = 1/8
And the opposite is
1 - 1/8 = 7/8

The second way is easier (1 permuation of events) than figuring how many permutations of events you're actually interested in (7 permutations).