Simplifed Poker Mathematics

Things you should really know to improve your play:

EV: Expected Value, also known As Equity

This is the amount you can expect to win over the long run.  This includes making the right decisions both pre and post flop.  A study of Position adds to this, so your starting hands should match your position.  How often have you seen an over eager opponent go all in or call all in with an AJ in early position?  Repeated over and over, this play leads to negative EV.

Some Starting Postional Hands leading to positive EV:
  • Early Position:  JJ, QQ, KK, AA and AK
  • Middle Position: 99, TT, JJ, QQ, KK, AA, AQ, AK
  • Late Position (CO, Button):  77, 88, 99, TT, JJ, QQ, KK, AA, KQ, AJ, AQ, and AK

In the blinds, it is sometimes profitable to call a raise with suited Ax (if no one else as entered the pot or reraised).  One on one, this can be a good play.

Study of Opponents:

This is very important.  I noticed one guy just raising and shoving.  At a single table on full tilt, not the rush game.  Since I wasn't using Huds,  I called with Premium Hands.  Always won (he kept reloading), and someone else did also.  EVERY TIME he raised and shoved, didn't matter the flop, it was either J9 suited, or J9 off suit.  Keeping notes on your opponents is very important.

If you have this kind of fish at the table, try to play tighter.  Late position also offers opportunity for suited connectors, but not against this type of player.  If you don't hit anything on  the flop (Pairs, OESD, flush draw), then you are just gonna have to give the pot up.  So your EV will take into account your opponents plays.

Don't ignore the math over your opponent.  Huds can't give you everything if someone decides to go on tilt, or only calls the flop with a single bet every time, and flopped the nuts.  Certain plays and changing styles of players renders the Hud not realistic.  So you need to learn to read your opponents (watch the multitabling here), and let the style of player influence your calculations.  Your Pot Odds and EV go up against loser player, and go down against tighter player.

Purpose of EV:

The goal in poker is to win over the long run.  Your AA may get busted a time or two.  You may be on long losing streaks.  But if you make the right decisions, you will win over the long run.

Pot Odds:

Basically, determining your number of outs, using some division, and calculating the amount of the pot (which includes your opponents bet), that you need to call for profit.  MANY players ignore this very important step.  Here are some examples:

You flop a Flush Draw, 9 cards for outs, against 35 cards that don't (9 handed).  Its 4 to 1 against, need 4 to 1 pot odds to call.  If you don't make your flush on the turn, odds are going down.  If the Pot is one on one, imagine Pot 1k, opponent bets 500, total pot 1500, only getting 3 to 1 if call.  To maximize expected value, should fold.

Pre Flop, you get big pocket Pair (99 or 10-10 in later position for example).  Blinds 100, 200.  You raise the typical 600, a 2000 chip stack goes all in, blinds fold back to you.  To call: 1400, Total Pot before your call:  2900.  2900 to 1400 is 2 to 1. If hand has 30% chance or better of winning against opponents range of hands, you should call.  If opponent has overpair (such as AA or QQ), chance of winning is less than 20%.  If opponent has AK or such, then chance of winning is over 50%.  Over Opponents range of hands, should probably call with Pocket 99 or better, have 33% or better odds to win (approx. 50 + 20 / 2).  Calling is right, because the pot odds are bigger, than the odds against you winning the hand.  Gives Positive Equity, Positive Expectation, for making the call.

OESD's (open ended Straight draws), combined with a possible flush draw (suited connectors), are better for pot odds.  You call with 10h-9h in late position.  Board comes 7h3s8h.  How many outs do you have 9 handed?  Well, start with 9 for the flush, 8 for the straight.  But hold on, 2 of those 8 cards are hearts (of course, this would be a straight flush draw), so for straight, have actually 6 cards that are not hearts to help.  Add 6 + 9 = 15.  A simple way to calculate your odds are - (Total Outs x 2) + 2.  This is roughly the percentage of making your hand.  Our calculations for this hand would equal 32%.  If this is the flop, see our above example for big pocket pairs.  With 15 outs on the flop, and hand one on one, odds are .9:1, in your favor, a call would be appropriate (even a bet if you are first to act).  However, by the turn, your hand is losing value, and the odds are 2.1:1 against.  Since the player is behind you, depends on size of bet, I would call if getting 3 to 1 odds on pot, and it doesn't put me all in.  (as to the Straight Flush draw itself, you only have 2 outs, a 6% chance of making that hand - but it does happen).  Making the right plays and calls using Pot Odds increases your +EV exponentially.

Implied Odds:

Implied odds are like Pot Odds, however, you are thinking about the money you can win on later streets (this is especially crucial in our example above with 10h9h call).  Pot odds imply no more betting, but there is another round or two of betting.   Consider what you might win as the hand progresses.  Implied odds are what you may win in the future with your hand, and are usually bigger than the pot odds.  Take more risk, and play more ranges of hands, because of implied odds, rather than just relying on pot odds.  Try to guess how much your going to win, if you do hit your card.

When thinking About Implied Odds, Consider the following:

How strong your opponents hand is, and how scary the board will look, when you hit or make your hand. For example, you have A hearts, and 4th heart hits the board.  You probably won't get paid off too much here.  An obvious draw will not get paid off often.

Hidden draws more profitable, OESD more profitable, opponent pays a lot more money, than if its obvious you hit a hand. Pay attention to previous streets, if you think Opponent has big pocket pair (the strength of opponents hand), the bigger the hand, the more likely he is to pay you off. - If you hit your flush or you hit your straight.

For Example:  Call 76 suited in position against AK, flopped OESD, rainbow, hidden draw, opponent has top pair top kicker.  Only have 8 cards against 45 to make straight.  Need better than 4 to 1 pot odds to justify calling.  Implied odds can justify calling, even though 3 to 1 pot odds, because opponent will probably pay off, if hit on turn.  If figure getting an extra 1500 if hit straight, actually getting 5 to 1 to call.  If opponent has 10-10, or AQ bluff, probably won't get paid off much.  But if opponent flopped set, get paid off big time.


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