Wednesday, July 9, 2008

Drawing dead pre-flop

Can you be drawing dead pre-flop? This had been discussed a couple times before, once at the lunch game and another time at Tuesday Night Poker. I had a solution where a hand couldn't outright win the hand but Ryan said that the hand would chop if the board came out Quads with an Ace kicker. I asked for clarification on what "drawing dead" meant and Ryan said that there is no way for the hand to win any portion of the pot whatsoever, a definition I agree with.

Fast forward a few weeks and as I'm getting my stuff put together to head out for the day it dawns on me.

KcKs - "Hero"
KhHd
AcAs
AhAd
TcTs
ThTd
5c5s
5h5d

At this eight handed table, Hero picks up two black Kings yet he cannot lay claim to any part of the pot regardless of which five board cards come. In fact as long as the hand does not have an Ace in it, it is possible to be drawing dead pre-flop. JhJc, 6s7s, 9h2d, 5s5d, doesn't matter, they can all be guaranteed losers.

13 comments:

Austin said...

I never thought about drawing dead pre-flop, that's kind of depressing. Your math looks mostly correct except for one thing.

You state at the end that any two cards can't win and are drawing dead pre-flop, which isn't necessarily true. If they hit quads, they would be winners.

Still, ugh, that's kind of gross to think about.

Ryan said...

Martin is saying that given any two cards, he can construct a preflop scenario in which they can't win; i.e., other preflop holdings make quads impossible.

Austin said...

Ah, ok, I see. Gotcha.

Sushi Cowboy said...

@Austin
Yup, what he said. You can basically generalize the scenario to AA, AA, TT, TT, 55, 55, and someone holding a pocket pair that matches each unique rank of your hole cards. That will do it.

It would be possible to construct hole cards so that someone with an Ace couldn't outright win but there will always be the scenario of Quads/Ace kicker to allow an Ace to chop. Well...kinda. I haven't fully worked this out yet but I'm pretty sure that if you allow a 12 handed table you could make an Ax hand be drawing dead too but I think a ten handed table should really be the limit for this exercise.

Sushi Cowboy said...

Son of a B! That ol' Internet thingy ends up giving an even better answer.

KcKs - drawing dead
AcAs
AdKh
AhKd
QcQs
7d7h
7c7s

Brilliant! I love how this solution handles the SF chops by including the high end (7 and K) so no one can play the board and saves from having to include the TT pairs.

jason said...

Definitely should consider folding Kings preflop 10 handed with 8 hands going to the flop and lots of preflop action. Could be drawing dead as you point out. But more importantly likely to be Aces out there.

According to cardplayer the odds of someone having aces with 10 hands preflop and you have Kings is 3.8% to one. This seems a bit high to me but I imagine the math is correct. The odds of someone having aces then deep stacked, meaningful stakes, with a limp reraise is of course much greater than 3.8% to one, but definitely hard to quantify.

jason said...

Also, I don't believe you can construct a scenario, 8 handed to the flop, where you are drawing dead with mid range suited connectors like 8,9 suited or TJack, suited.

Sushi Cowboy said...

Jason, it's not 3.8 to 1. It's about 4%. The odds of being dealt AA is 1 in 221 hands or about .4 percent. Therefore at a ten handed table the odds of someone having AA is ten times that or about 4%. The fact that you happen to have Kings during one of those times doesn't change the odds of someone else picking up AA. Now if you had AA, then the odds of someone else having AA is dramatically changed.

As for the drawing dead hand, my generic formula won't work for suited connectors. So for 8d9d, instead of AA, AA, TT, TT, you just need to make AT, AT, AT, AT of each suit so that any Flush will lose to a higher Flush, and add in 88 and 99 to eliminate Quad possibilities.

jason said...

you are right I meant 3.8%, not 3.8:1.

Sushi Cowboy said...

Drawing dead in Omaha or O/8 is easy. Just run 2c2d2h2s up against 3c3d3h3s.

Don't think it's possible in Stud games. I'll have to think about it some more.

Sushi Cowboy said...

Drawing dead in Stud.

For Hi, there is always the possibility of running Quads so can't draw dead in Stud Hi at a standard 8 person table.

Razz, you can be dealt rolled up Kings as your first three and still make an A234K which could be good enough to win. The other player's starting hands cannot be guaranteed a better Razz hand than that.

Stud/8, you can start with three high cards to eliminate any claim to low but you can still catch running Quads.

So, bottom line is that you can't be drawing dead on third street in Stud Hi, Lo, or Hi/Lo.

LewTree said...

Bump.

If you changed both pocket kings to pocket 9s then four hands, the ones holding pocket 9s and the ones holding pocket Ts would all be drawing dead before the flop.

Wingpin said...

What id the board was 23456 ?