Hold 'Em - what's the best chance you'll be outdrawn?

[JerseyTom]

Hi all,

I got to thinking about this while goofing off at a play money no-limit table. Apologies if something like this has already been posted.

I have A /images/graemlins/heart.gif T /images/graemlins/club.gif and the flop comes K /images/graemlins/diamond.gif Q /images/graemlins/diamond.gif J /images/graemlins/spade.gif, giving me the nut straight. Now we all know how to look for monsters under the bed (and it only takes one monster to crush your hand), but I was wondering...

Given this exact flop and the cards in my hand, what exact combination of hands could my opponents hold that would give them (collectively) the best chance at outdrawing me? We would want minimal (or no) overlap in my opponents' outs in order to maximize "the field's" chances. Note too that my hand cannot improve, so we might additionally consider split pots as "partial losses" (e.g. runner-runner A-10 to put a straight on the board).

I don't have an exact answer for this, just a few ideas, but I'm curious how others would approach it.

I forget exactly how many opponents I had, but let's assume I had 4 (small enough number, yet big enough number?) leaving 39 cards in the deck after the flop.


Tom

[SossMan]

I think pocket kings and AT /images/graemlins/diamond.gif pretty much cover all bases.

[Lost Wages]

You need to add a hand with 2 spades.

Lost Wages

[Nottom]

If you allow for opponents to have AT then I think the worst case is

K /images/graemlins/heart.gifK /images/graemlins/club.gif
A /images/graemlins/diamond.gifT /images/graemlins/diamond.gif
A /images/graemlins/spade.gifT /images/graemlins/spade.gif

pokenum -h ah tc - kh kc - ad td - as ts -- kd qd js
Holdem Hi: 820 enumerated boards containing Js Kd Qd
cards win %win lose %lose tie %tie EV
Tc Ah 0 0.00 547 66.71 273 33.29 0.111
Kc Kh 266 32.44 553 67.44 1 0.12 0.325
Ad Td 252 30.73 295 35.98 273 33.29 0.418
As Ts 29 3.54 518 63.17 273 33.29 0.146

If you add the requirement that you are ahead on the flop I think the worst case is something like

K /images/graemlins/heart.gifK /images/graemlins/club.gif
T /images/graemlins/diamond.gif9 /images/graemlins/diamond.gif
A /images/graemlins/spade.gif9 /images/graemlins/spade.gif

pokenum -h ah tc - kh kc - td 9d - 9s as -- kd qd js
Holdem Hi: 820 enumerated boards containing Js Kd Qd
cards win %win lose %lose tie %tie EV
Tc Ah 210 25.61 546 66.59 64 7.80 0.295
Kc Kh 264 32.20 554 67.56 2 0.24 0.323
Td 9d 254 30.98 541 65.98 25 3.05 0.324
As 9s 28 3.41 751 91.59 41 5.00 0.059

[Zetack]

He said four opponents and any pocket pair could make a runner runner boat or quads...shouldn't you include one of those?

--Zetack

[Nottom]

The set of Kings already has that covered.

Any hand you add is just duplicating the outs of the others so I suppose as long as it doesn't take any away from the flush draws it wouldn't really affect the results much.