Thursday, March 17, 2011

Just Playing Math in Texas Hold'em

I love this subject because it's the math of poker.  In my Friday Night Games, I started saying, "I'm just playing math."  It's really maddening sometimes to know the math of poker, especially the odds of hitting draws (or really the odds of hitting any card).  It's maddening because of how much fun it is to play and not fold, but smart poker relies on playing the odds.

Many of the guys I play with regularly REALLY like to have fun playing poker - I mean seriously, really like to have fun.  And the trade off to fun is WINNING in the long-run because smart poker requires folding and not getting involved in many hands. 

What?  Folding!  And then there's Friday Night Poker.  I'm not risking all that much to play with my friends, so it's OK.  But, like I said, this is a fun topic and I'm going to write about it anyways. 

So, the odds of hitting draws on the river are really, really bad.  It's the rule of 2 which says that you multiply your outs by 2 (with only the river card to go) and that gives you the percentage chance of success.  So, the best possible draw you can have is an open-ended straight draw, along with a flush draw, and add that one of your hole cards is an Ace that if it hit could possibly win the hand.  So, you have 4 cards to a flush already, leaving 9 other flush cards.  Add to that 6 of the remaining non-flush cards that could make your straight, and the remaining 2 non-flush Aces and you've got yourself a solid 17 OUTS.

Now multiply those 17 outs by 2 and you get a whopping 34% chance of hitting a winning hand.  That's basically a 1 in 3 chance of success, but a 2 in 3 chance of failure.  But wait!  What if you're up against another flush draw hand or another open-ended straight draw hand and that person hits too and has a higher flush or straight?  Well, now you're just screwed all the way.  You might think that a scenario like that is too unlikely to really happen and true, the odds of that aren't super high, but I've seen it.

Last week, I saw 2 guys hit a Jack High Straight by the turn and river, while a 3rd guy also hit his Jack High Straight on the River (seriously, this really happened).  Guess what?  Guy #3 actually made a Jack High Straight Flush and won the hand.  The really sick thing about that, is that his odds of hitting that Jack of diamonds were about 49 to 1 against, but for some people, hitting that hand is all they need to chase cards for the rest of their poker lives.

But back to our 2 out of 3 chances of failure scenario.  The only way you can make a call where 2 out of 3 times you will fail is if you get more than those same odds in the pot.  So, you need to make 3 to 1 or more on your money to even consider calling river bets.  And there you go playing math again.

At a game like I play on Friday nights, you have 4 to 6 guys that are generally willing to call down to the river - regardless of the odds.  If you have 1 or 2 guys who do this, then you have a very profitable game in the long-run, but with 4 to 6 people doing it, you're very likely going to simply lose your mind.

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