I think these numbers are fairly close.

How often TT flops a set and AA flops a set: 1.02%
How often TT and AA have a set on the river: 3.09%
How often TT flops a set and TT & AA have a set on the river: 1.92%

Here's someone who seems to have a general idea of the math:

http://archives1.twoplustwo.com/show...=0&page=2&vc=1

He recognizes that pre-flop and post-flop dollars aren't the same so he has to be sharper than the average person.

Show your work.

I used a home-made tool. As I said, if you have Visual Studio and know C#, I'll be glad to share the code that "proves the posts".

If I had it to do over again, I'd post a link to a PokerStove tutorial and leave it at that. Tools make life so much easier. Anybody who knows that PokerStove correctly handles boards where only one or two cards are known has to be okay: http://www.cardschat.com/poker-stove.php

I have good news and bad news. Good news I found another tool that properly handles boards where less than three cards are known. The bad news is that it produces the exact same values as PokerStove.

You can specify the flop as Tc**, *Tc*, **Tc and you get the same answer. Even ***Tc works and produces the identical answer.

http://propokertools.com/simulations...2=AA&s=generic

Can you please explain the odds of 4 people flopping a set? i must have missed this in reading through the thread...

So, smmcoy is saying that the odds of set over set on the flop is 4.81:1 when there are only 4 cards available to make that possible.

If I hold KJ, the odds of me flopping 2 pair [with 6 cards available] is ~48.5:1.

Here's a simple way of doing it:
I have AA & you have KK. The board has to come AKx as we are not concerned with permutations.

So, for the A & K, that's 2[aces]*2[kings]=4 & then multiply that by the remaining cards in the deck that are not an A or K [2]. 4*44 = 176 possible flops for set over set.

176/19600 possible flops = 0.8979%

Or, you can say: We know I hold AA & you hold KK, so there are only 48 cards available for the flop. So, [48*47*46]/6 = 17,296 possible flops.

176/17296 = 1.01757% & Presto! You've come up with almost [1.5625%] the same answer that you get when you multiply .125*.125.

Think about it. If you flop two pair 2.02% of the time, with 6 possible cards to make it come true, you must flop set over set much less often since there are only 4 cards available to make it come true.

It doesn't matter if the correct answer is 0.8979% or 1.01757%, or 1.5625%..........Just so long as it's clear to everyone that smmcoy's answer of 17.2% is not even in the same state.

This can be dangerous though, and lead to the problem we have to account for of spewing a street or two when we don't flop a set. If we're constantly calling a cbet on a 9high board and just hoping he doesn't continue on the turn (or calling some turn bets, or even sometime continuing on to call some river bets), it's leaning towards spewy, and thus we need bigger implied odds to make up for these times that turn out bad.

GcluelessspewynoobG

They're correct if quads don't count, and ignoring straights and flushes.
Not quite. Just take the 3.09% and multiply by 3/5 because, of the times a T hits the board, 3/5 of the time it will be on the flop instead of the turn or river. So the percentage is 1.856%

Edit: nvm the above reasoning I just used is flawed.

Edit #2: wait I think I was right, lol hold on I need breakfast and tea.

Yes this is right.

I got confused because after that, I was about to say that you could also get the 3.09% by multiplying 1.02% by 10/3, but when I tried that it didn't work. But the reason that didn't work is because it allows the turn or river to give someone quads.

Wow... I'm digging this thread. My statistics skills are rusting but I'm liking the empathy, garrick, smmcoy, and lapidator posts. The numbers are getting a bit hairy at times when you guys go deep into the math, and convolute the main purpose of the discussion. But all four posts are confirming each others numbers. ~2% of the time you have a PP and face a bigger PP you will set up and lose. ~ 18% you do set up, you will lose to that bigger pocket pair.

Thanks for all the effort guys.
Kookiemonster... Look what you started BUD lol

More like 3%, even without including quads possibilities. Smmcoy got 3.09% with his software and I got it with math:

2*2*C(44,3) / C(48,5) = 301/9729 =~ 3.0938%

(Edit: unless you meant "you'll flop a set and lose", in which case yes it's about 2%. It's 1.856% not including quads, so with quads it's even closer to 2%.)

Yes, but don't be mistaken about what this is saying. If you flop a set and he doesn't, you're definitely better than 82% to win. He has two outs twice which does not equal 18%.

What it's saying is that if the 5 board cards are dealt face-down, then the dealer turns one of them up and it's your set, there's roughly an 18% chance that one of the four other cards gives villain a higher set (but not quads, so the chance of losing is slightly higher since it would include those).

Yes, but don't be mistaken about what this is saying. If you flop a set and he doesn't, you're definitely better than 82% to win. He has two outs twice which does not equal 18%.

What it's saying is that if the 5 board cards are dealt face-down, then the dealer turns one of them up and it's your set, there's roughly an 18% chance that one of the four other cards gives villain a higher set (but not quads, so the chance of losing is slightly higher since it would include those).

Cool, yeah I've got that. I'm not really digging that 1 by 1 by 1 by 1... view of it. I treat the flop as a 3 card unit, he either flopped it or he didn't. I have no need to argue over this tho, the numbers are what they are and should be considered accordingly. (I'm usually the one nerding out like you guys are, so I appreciate you clarifying the difference.)

Also, I'm being lazy here. Is the 3% that TT and AA both have sets by river assuming that TT will stick around to see a river 10? (Lazy meaning I don't want to read back through all the posts, because I thought we had multiple confirmations on the ~2% with the assumption TT is purely set mining and quits when missing on the flop.)

Probably because you're thinking in terms of what's useful. The "1 by 1" scenario is purely hypothetical and the 18% stat can never be useful since there's no round of betting after seeing just the window card. The potentially useful stats are preflop and at a full-flop because those are decision points.

Yep, and you're right that the 2% is when TT only setmines.

I don't know how you guys managed to salvage this thread. Good job. I have never seen Mpethy trolled that hard. It was approaching epic.