Understanding odds in a poker game is vital to a successful poker player and must be learned by all who are serious about winning. I will present and explain the three vital statistics that make up a poker game, pot odds, implied odds, and "outs".
Hand odds (outs) or more specifically the odds of making your hand, or odds of your hand being beat on the next card. This represents those percent numbers next to people's hands when you watch poker on television. This is vital not only in determining whether your hand is good or not, but the odds of making that straight, flush or higher pair.
When playing a game, you can only guess the kind of hand someone else may have and thus the only true odds you can calculate are your own odds of making a hand or odds that someone else may make a hand (if you suspect they are on a draw).
To calculate these odds you take the number of "outs" that you have, these are cards in the deck that can still help you, and multiplying by two. This is the odds that one of your outs will hit the very next card.
For example: You hold Jack Ten off suit (both cards have different suits), the flop comes KQ2 rainbow (3 different suits). You determine that you are more than likely up against a pair of kings or queens. Thus in order to win this hand you will need to complete your straight with an Ace or Nine. You have 8 outs in this situation, 4 aces and 4 nines. This means you have a 16% chance or about 1/6 odds to make that straight on the turn. You have 32% or 1/3 odds to make that straight by the river.
Similarly with a flush draw holding 4 of the same suit, you have 9 outs in the deck to hit one of the remaining flush cards. This would translate into 18 percent or just a little better than 1/6, again you double this to figure your odds of hitting this hand by the river.
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Pot odds are where you take your knowledge of counting outs and apply them to deciding when to call or fold your draw. Pot odds are actually much easier to calculate than your figuring out odds based on your outs.
Pot odds are simply the amount you must wager to win a certain amount of money. For example if you have a pot with 6 dollars in it, and someone raises 2 dollars you will be getting 1 to 4 on your money. You are wagering 2 dollars (your call) to win the 8 dollars in the pot (6 in the pot plus the 2 dollar bet).
So what exactly does this mean? Well traditionally you should only call this bet if your hand has 25% or better odds of winning or 25% or better odds of making your hand on the next card. For example with our straight and flush draws in our previous example, neither would be adequate for calling on the flop. Or are they? In my personal opinion you have an adequate hand to call this 1 to 4 pot odds bet and this will lead us to the next topic: Implied Odds.
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Implied Odds are similar to Pot odds, but they are the odds based on money you could win by the end of the hand. For example, both you and your opponent have 10 dollars in the game, and he bets the same 2 dollars into the 6 dollar pot. Thus he now has 8 dollars in front of him, and there is now 8 dollars in the pot, thus you have the potential of winning 16 dollars in total, giving you 1 to 8 or 12.5% on your money.
If you believe that you can extract much more money out of your opponent by the showdown if you do make your hand, then this is now an adequate call with a flush or straight draw.
If you are playing a Fixed Limit game, then implied odds become much more difficult to accurately calculate. This is a very important thing to remember when playing limit, pot limit and no limit poker.
*****Edit June 5th*****
I was asked to further explain implied odds in fixed limit games and why it's more difficult to calculate them and use them in your poker math. The reason is that it is very difficult to calculate whether you will have someone who will call you down, reraise you, or fold by the river. Thus relying on implied odds to make your decisions is much more speculative.
In my own personal opinion you should only rely on pot odds when making plays at fixed limit poker. And often because of it's fixed limit structure you will be given correct odds to chase your flush and straight draws anyway. If you really want to include implied odds in your decision making process then I suggest taking your current pot odds and making it slightly bigger. For example if your pot odds on the turn with a draw is 1/6 you can probably safely say that your implied odds are around 1/7 or 1/8. Again I personally wouldn't advise making too many decisions on implied odds in fixed limit poker.
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Bringing it all together:
Learning the math of poker takes some time and practice, but it’s vital to your play. It will keep you from chasing hands given bad pot and implied odds, and seemingly chase hands that you might not have before.
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What may be more important to note is that you should always make the pot odds for your opponent large enough to cause them to make mistakes and chase hands they shouldn’t if they figured the math correctly. This is why it’s general practice to bet 1/2 to full pot bets if you are going to bet or raise your hand. 1/2 pot bets will give your opponent 1 to 3 pot odds, and full pot bets will give your opponent 1 to 2 pot odds.
This is why it’s very important to bet your big hands aggressively, because players calling these bets with inadequate hands will be seeing flops, turns and rivers without the right pot odds and in the long run will lose money to you.
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Implied Odds will explain why we will see small pocket pairs for cheap before the flop. For example, lets consider we hold pocket 8s in a 1$/2$ NL game. Everyone in the game will have stacks ranging around 200$, thus you are getting 1 to 100 implied odds to limp pre-flop, and you are still getting stellar implied odds to see a flop for 2-5x the big blind (1-50 to 1-20).
You will connect with your set around 1 out of 8 times, and you will make that set on a “non-scary” board (a board with no straight and flush potential) around 1 out of 10 times (note: rough estimate). Thus this makes these hands incredibly profitable when you make your set as you are more than likely going to be paid off by the showdown if played correctly.
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In conclusion, learning these basics will help to make you a good poker player. However, if you just enjoy playing poker, and enjoy the gambling aspect of the game, then by all means disregard all the tedious out counting and figuring out your odds and play however you like.
If you do count your outs and figure out your odds, but happen to lose, don’t fret, if the math adds up, you made the correct play and you just didn’t get lucky. To avoid tilt, you must focus on your long run results, and realize that if you played that hand 100 times over with random flops, turns and rivers that you will net a profit.
Your long term results rely on good play. Short term results are at the mercy of lady luck.
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One thing I’d like to note is that you should never tell someone what to do at the poker table, everyone is at the table for their own reasons, whether it’s to play seriously or for fun. To tell anyone differently is rude and unnecessary, and if I personally owned a poker room I would not hesitate to eject a player for being rude or berating another player’s game. Let the gamblers be gamblers, and let the fish swim.
Anyone who berates the play of another player can never be classified as a good poker player, as it’s analogous to the shark advertising to the pool of fish that he’s on his way to eat them, and telling them they should swim faster. It will only make it that much harder to win their money if you criticize the play of another at the poker table.