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Although the concept of mathematical advantage has come up in many lessons so far,  we'll look into this in a bit more detail in this lesson.  Essentially, mathematical advantages are what poker is all about.  In casino games, like blackjack, roulette, craps, slots, and the like, the house has the mathematical advantage.  The games are set up that way of course.  Although a player may win in the short run, their mathematical advantage guarantees them that in the log run they will win money.

With casinos though, the advantages are pretty slight.  But they do add up to a boatload of money a year for each of them.  As dedicated poker players, we're after the same sort of advantage, and actually, the advantages that we can gain will be higher percentage wise than other casino games.

Thus, poker, unlike most other forms of gambling, is a game of skill.  And we use our skill to gain the advantage over other players.  And this skill essentially comes down to mathematical advantages.

So the first thing we need to realize is how important this stuff is.  Whether we like it or not, we are dependent on the math of our play.  Most often, players will come up with rules or guidelines that do take advantage of this (for instance, playing tight), but the connection isn't explicit.  If we're going to take full advantage of the situation though, it needs to be.

And this is going to permeate every aspect of our play.  Sure, things like pot odds are going to play a role, but this isn't the extent of it at all.  We want to calculate our chances for any given round and for the hand as a whole based not only on our cards, but how many players are in the pot, and the specific playing styles and patterns of all our opponents.

There are two stages to this.  First, we want to know where we're at against a random hand, in reference to how many players are in the pot.  With experience, we will develop a better and better idea of this.  Or we could use a program like Poker Pal, which calculates this for us while we're in a hand.  Even for experienced players, this is a valuable tool, especially if you're at a table with less than 10 players.  I've used this software for quite some time myself and I highly recommend it.  If you're interested in checking it out, click on the banner for their site towards the bottom of our home page.  I've worked with them in helping improve their software, and it's a handy tool to have and not very expensive for the benefits it gives you.

However you do it though, you need to know what your chances of winning a hand at any given time is, against random hands.  Now this doesn't mean that our work is over though.  We have to place this information in context of what our opponents may actually have, and what they are likely to do.  And we'll be using math to determine both.

Aside from the type of hands our opponents play (high cards only, high card flush draws, suited connectors, small and meduim pairs, unsuited connectors, etc), we can get a glimpse of the quality of their hands by paying attention to how many they play.  The player who is seeing every flop, for instance, can have pretty much anything.  So we will put him on a random hand to start and then pay attention to his betting patterns to refine our determinations from there.  On the other hand, if a player plays very few hands, we can use this to put him on a certain quality of hand pre-flop, and one that is quite a bit higher than the norm at the table.  Therefore, when we go against him, he's often going to have better than a random hand and we will need better hands to beat him.

We need to look at tendencies for each particular betting round to get a good feel of where we're at here though.  For now, we'll take a fairly tight player, who plays about 1 in 5 hands, and go through the thinking processes here a bit more, to get an introduction to some of the concepts we'll be using.

We know this player plays about twice as many hands as we do, so we've got the advantage going in.  And he raises about 1 time in 10, so when he raises, he's about in the range we play.  So if he doesn't raise, and we have a playable hand, we're going to have the advantage over him most times.  If he does raise, we're going to need to have the better of our hands to call him.  The top half of them will do here.  We also know he'll re-raise  1 time in 20, so we'll need something even better - a high pair - to call these, and still maintain our mathematical advantage over him.

In these examples, what we're looking for isn't to win every hand of course, but to beat him more times than he beats us in all these situations.  That way, over time, we're taking his money.

Now, on the flop, he's going to have something about 1 time in 4, we'll say.  And we'll have something about 1 time in 3, since we're playing better cards.  And if we have something, since we have the advantage, we'll maintain that advantage more often than not.  This is why it's so important to be selective pre-flop, and make sure you start out with the advantage. 

To illustrate this a little more, let's say we have AJo, and an ace flops.  We know he probably doesn't have AK or AQ, since he probably would have raised earlier.  So we've probably got him beat at this point, and whatever he has, if you play this out 100 times, say, we'll make more money off him than he will make off of us.  So we have the mathematical advantage.

Now, we've got position on him here, and he bets it out 3 out of 4 times in this situation, say.  It's just the 2 of us in the pot, and remember, he only hits his hand 1 time in 4.  So the other 2 times he's betting, and he hasn't hit much.  So what do we do here?  We raise, because chances are he's bluffing.  If we get re-raised back, then we may be beaten in this particular instance.  However, if he folds or just calls, we've got a good chance to win the hand by hitting something later, or even by winning with high card.  This is because, since we started out with the advantage, any time neither of us has anything, we're going to have the better hand more often than not. 

So this gives you an idea of some of the things we're going to be thinking about during the hand, and in particular, the importance of starting out with the mathematical advantage by being more particular about what hands we play than our opponents.  This continues throughout the hand as well.  We'll look into all this more in later lessons.
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