Outs & Odds
You have already played poker for a while now, you know about the rules, and which hole cards can be played, but now you want to enlarge your knowledge about this beautiful game? - So the next step is to learn how to calculate the chances of your current hand becoming the winner hand.
Before you can do so, you need to know the term "out". One "out" in poker describes one card, which is still in the deck, and would help you to make your hand the best, if it would come among the next community cards. Each of these outs can be multiplied approximately with 2% probabiliy, so the odd for each card is 2%.
Exampe: Calculation for 4 suited cards, chance to receive the flush
On your hand you are holding the ace and a 7, both in diamonds. The 3 cards from the flop are already on the table: 2 in diamonds, queen in clubs, 9 in diamonds. So you have 4 cards suited, but for a flush, it would need to be 5. Of course you hope to see another diamonds card on the turn or the river (4th and 5th community card).
You know 5 cards: your own 2 + 3 community cards, which means that there are 47 unknown cards, which are still in the deck, or one of your opponent has them.
The following cards would bring you the flush you are hoping for: Diamonds: 3, 4, 5, 6, 8, 10, Jake, Queen, King; altogether 9 cards, which would make your hand most probably to the best one on the table. Those 9 cards are therefore 9 outs, multiplied by 2% each, you have an odd of 18% to hit the flush on the turn. As there is another chance that a diamond card will be shown on the river, there are another 18% chance.
Combined you have a chance of about 36% to get the strongest hand in this situation, or in other words: the odd is 36%.
Example: Calculation with a pair, making it to three of a kind or 2 Pairs
Dependent on the number of active players on your table, and the already open communicty cards, even a weaker combination, for example even three of a kind, might become the strongest hand.
For example: your hole cards are queen, clubs and 7, hearts. The flop shows 3, diamonds, 7 in spades, and the ace in hearts. So you hit a pair of 7 on the flop. This is possibly not the best hand, as somebody else might have another ace in his hand, and has a higher pair. But your hand might become the strongest, for example if another 7 from the deck would be uncovered. As you already see two 7, there have to be another 2 left in the deck. This means 2 outs for you, which results in an odd of 4% to get your three of a kind on the turn, another 4 % on the river, and 8% combined.
Are there few players on the table, even the combination 2 Pairs would be the best hand. In this situation, you would have 5 outs, (10% chance on turn/river, or 20% chance combined), as you can calculate the 3 missing queens additionally to your outs.
Additional Information:
Why is each out approximately 2% odd?
It is a very simple calculation: Each card, that you don't know, whether it is your opponents, or still in the deck is seen as the same. After the flop you know 5 cards, and you don't know 47. The exact calculation for one card that can help you would be:
1/47 = 2,13%
On the river it would be 1/46, as you know one more card.
The exact calculation for the chance to hit the flush on the turn, with 4 already suited cards is:
9/47 = 19,1%
The calculation always is the outs divided by the unknown cards.
