Picked Doyle Brunson's SS/2 from my shelf yesterday and browsed the PLO section. It is a great chapter (perhaps a little too oriented to the high stakes player) and provides some valuable insights. Towards the end of the chapter there is a chart + explanation of the effect of 'Kill Cards' and how these can lead to people overestimating the odds of hitting a draw.
Here is a basic explanation - you have 9-10-j-Q double suited (an excellent PLO starting hand!) and call a raise before the flop which comes A-8-7. You bet and your tight opponent re-raises, knowing this opponent you can safely put him on trip aces... yet you have a wrap. The question concerned working out your odds of hitting your straight draw (we'll ignore flushes for the moment to keep things simple).
So you have a total of 4*6's, 3*9s, 3*10s, 3*Js here on the turn - a king coming on the turn would even add more 3*Q on the river.
Turn Outs = 13
River outs with a K on turn = 16
Thats a good number of outs - there are 46 unseen cards (we are never sure exactly what our opponent holds) which might indicate that we are 50/50 to win the hand if all the money were to get in right now... any overlay from the pre-flop betting round making this a positive expectation play over time.
However, what about outs for our opponent? Assuming he does have trips there are several cards which could come which would 'kill' our draw. These are known as the killer cards in pot limit omaha strategy... the question is not that they exist - but how (mathematically) do we account for the effect of our chances of winning the hand. In this case there are 7 killers on the turn (any 8, 7 or the remaining A) which will give our opponent a full house. On the river this goes up to 10 - even when we make our straight - as the turn card and river could be a pair also making that full house.
This is where Lyle Berman's Killer Cards Chart comes into play (will not reproduce it - copyright etc!) This gives numerical values which compare the number of outs the drawing hand has compared to the amount of killer cards the made hand has with which to redraw.
In our example the draw was in fact 53.9% to get there with 2 cards to come - the turn kill cards reducing this percentage to 42.8% and the river card even more. Food for thought -you would need 21 outs to be favourite with 2 cards to come against top set - even though so many cards help your hand the chance of any opponent redrawing to a full house or even quads reduce your chances significnantly.
Back to SNGs / Tournaments for the rest of the week - hope the PLO strategy posts are providing a little food for thought!