Friday, February 02, 2007

February 1st

Each day this month, I am going to attempt to learn something new about PLO or review an important concept that I previously learned. This first one (posted 2/2/07) is from yesterday:


Flop with 3 cards of the same suit.

I learned that the chance of someone having a flush when 3 cards of the same suit are dealt on the flop is about 19%, so I decided to try and apply it to an actual game.

I frequently run into a game that is very passive and tight post-flop. People usually represent the strength of their hand post-flop. There is not a lot of deception. If they have the nuts they will bet or re-raise. They have a draw, they might minimum bet but then call if you reraise. Or just call you, regardless of whether or not they have pot odds. I figured that if there is a flush on the board amongst these opponents and you represent that flush, there is a good chance that they will fold.

Let's take a look.

Say you are dealt a hand that has no hearts and 3 other people see the flop that has 3 hearts and a $5 pot. There is a 52% chance that someone has a flush.
http://forumserver.twoplustwo.com/showflat.php?Cat=0&Number=8854813&an=&page=&vc=1

(Another interesting article http://www.math.sfu.ca/~alspach/mag80/)

Therefore, I figured that if just 1 or 2 other people see a flop and it is all the same of one suit, there is <50% chance that someone has a flush. If I have been playing reasonably tight and my opponents are folding if they don't have anything, I figure that if I bet $5, and 60% of the time, I win the pot right there this move has positive expectation.

(0.60)*(+$5)= + $3
(0.40)*(-$5)= - $2

A couple of notes:
1. Position doesn't really matter for this play, I don't think. EP then your bet is more believable. LP then it may look like you are stealing.
2. I'd say in 1,000 hands I think I tried this 4-5 times, so we are talking about a situation that doesn't come along all that much.
3. I would guess the more you try this, the more likely you are to get called.
4. It may seem like if you were heads up, it may work more. However, even the dullest villain will know that the heads up you might be making a move.
5. Of course if you have some of that suit in your hand, it increases the chance no one has a flush.
6. If you actually have a non-nut flush, you have to think about this situation differently and you have other considerations, but knowing the chances that someone has a flush is useful
7. If your pot-sized bet doesn't take down the pot, it might be wise to release the hand. Whether or not to fire another, or two more, bullet on turn and/or river requires more analysis.

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