Combinatorics (very very long)

[bluffbetter]

The 6 ways is because there are 6 combinations of suits for each pair. e.g.

A [img]/images/graemlins/diamond.gif[/img]A [img]/images/graemlins/heart.gif[/img] ..........A [img]/images/graemlins/diamond.gif[/img] A [img]/images/graemlins/club.gif[/img]
A [img]/images/graemlins/diamond.gif[/img] A [img]/images/graemlins/spade.gif[/img] ..........A [img]/images/graemlins/heart.gif[/img] A [img]/images/graemlins/club.gif[/img]
A [img]/images/graemlins/heart.gif[/img] A [img]/images/graemlins/spade.gif[/img] ..........A [img]/images/graemlins/spade.gif[/img] A [img]/images/graemlins/club.gif[/img]

[Nottom]

[ QUOTE ]
I just wanted to add for beginner combo counters that for pocket pairs the total possible combinations is 6 ways. I dont know what the calculation is, I believe it's a permutation though not sure, I'm useless at math.

[/ QUOTE ]

[mathgeek]
Technically its a combination. A permutation is when order matters, but since A[img]/images/graemlins/spade.gif[/img] A[img]/images/graemlins/club.gif[/img] = A[img]/images/graemlins/club.gif[/img] A[img]/images/graemlins/spade.gif[/img] we then divide the number of permutations (4*3) by the number of ways we can arrange each one (in this case 2) to get the number of combinations (6)
[/mathgeek]

[Antinome]

nice.

while combining this with equity calculations is implicit, some explicit examples would be cool.


Also the microscope metaphor- I tend to look at range->combinatorics->action as a series of filters that continuously narrow the range. I don't always do the combinatorics right, but in some of those really tricky spots in 3bet pots where the range starts narrow it is pretty easy and helps a lot.

[cooker3]

Great post.
This has been something I am thinking about more but too lazy too actually do it. It just goes to show how much I have to learn.
Sticky this plz

[Chomp]

Derosnec, could you post a hand where you think you used this in real-time at the table?

Cheers. Great post.

[kazana]

Love it. Thanks.

[Jouster777]

Very nice derosnec! This stuff really has a very small barrier to understanding and if people just read your post a couple times it WILL become second nature.

The combinatorics should be the easy part. Correctly assessing the dynamics of the hand (villain's play, PF, texture, our image, etc.) and then translating that to a range with proper discounting is the hard part. After that the combos are automatic (or should be). I hope this post gets more people doing it because it will raise the level of discussion on the whole board. Once someone goes through the trouble of dissecting a hand with combos, the discussion can switch to assessing the assumptions that went into the calculation rather than staying at the level of "well I always push here".

[corsakh]

Nice.

[Baintz]

Great stuff, muchos thanks for doing this.

[bozzer]

i read this last night, and it helped a lot - i didn't realise it was so easy to do.

I agree with Antimone that this is probably most useful in spots where ranges are very tightly defined - like in 3bet pots when an ace and a king flops or something.