Sunday, July 29, 2007

Playing Draws in No Limit Holdem - Kill Cards Revisited

After doing a post on 'Kill Cards' in PLO about 10 days ago I started to wonder whether this concept could apply to No Limit Holdem draws vs made hand situations too...

The concept is this: Most players know the post-flop odds of hitting a straight or a flush. To get this you are simply dividing the number of unseen cards that will help your hand by the total number left in the deck.... for the record here are some of the most common post-flop odds.

Approx odds of completing a flush with 2 cards to come (assumes 2 of suit in your hand and 2 on the board) = 35% (around 1.9/1)

Approx odds of completing open ended straight with 2 cards to come = 31.5% (around 2.1/1)

Right, so what about these 'Kill Cards'.... here is the idea - your opponent in each case has a made hand, trips, 2 pair or maybe top pair with a draw of their own. When this is the case there are unseen cards in the deck that may complete their draw to a better hand regardless of whether that (or the next) card helps you... your draw has been 'killed'

Will use the example of a flush against trips (pair in opponents hand rather than paired board). On the turn card you have 9 outs (the unseen cards of your suit) but here your opponent has 7 'Killer Outs'... for example 8-A-J on the board and opponent holds a pair of 8's in his hand, now the one remaining 8 and also any of the 3 remaining Aces or 3 remaining Jacks give him a full house....

Moving to the turn, even if you made your flush already your opponent has 10 more outs to beat you... the 8, 3*ace, 3*Jack and the 3 remaining cards that might pair the turn card.

Of course the question is not that such kill cards exist, it is how do we account for these in numbers - what are your odds of winning the hand after the flop in this example?

The answer here is that you have gone from being 35% to win the hand to 25.5% - from 1.9/1 to just about 3/1, big difference when thinking of a pot-odds based call in a tournament situation.

Of course you can not be sure that your opponent has trips (thats the beauty of the game after all!!). What about the same scenario where your opponent has top 2 pair - he now has 4 outs twice to make that full house, that is 4 of the remaining cards in the deck are 'killers' for your flush draw....

The effect is smaller, reducing your chances of winning the hand by just over 1% or from 1.9/1 to just over 2/1.

The situation could become a little more complex - if you have a straight draw against possible trips + backdoor flush... or even with more than one opponent with different draw / made hand combinations...

Will leave that for another day - hope to have given readers a little food for thought on the subject of Kill Cards in No Limit Holdem!

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