Basic Mathematical Concepts – Part 1

Outs

Outs are cards that, if they appear, will likely give you the win.

Example: You have :As :Ac and the flop is :Kc :Qc :Jc . You and the other player go all in and he shows that he has KQ. How many outs do you have?

Answer: 9 clubs – { :2c , :3c , :4c , :5c , :6c , :7c , :8c , :9c and :Tc }; two aces – { :Ad and :Ah }; three tens – { :Th :Ts :Td }

Note: Be careful not to count the T twice!

Why is this important? Because you can calculate your chance of winning. It's quite simple. After the flop and after counting your outs, you multiply by 2 to find out the chance of one of your outs appearing on the turn and multiply again by 2 to find out the chance of one of these cards appearing on the river. In other words: After the flop, in this hand of AA vs KQ, you have 14 (outs) x 4 = approximately 56% chance of one of your outs appearing on the turn or river.

Party Poker is back in Brazil! Learn about the bonus and benefits when creating your Poker Dicas affiliate account.

Pot odds

Pot Odds are like the contribution you make to the total pot. If there is 100 on the table and someone bets 50, you have to pay 50 to receive 200 in total, which is equivalent to 25%. Another way to calculate it is: The opponent bet 50 and now there is 100+50 on the table. I have to pay 50 to receive these 150, that is, the odds are 3:1 (which is equivalent to 25%).
Well then. Regardless of one's perception of the sport of poker, it is undeniable that mathematics plays an essential role in the game. Anyone who wants to take poker to a level beyond recreational knows that a play, to be profitable in the long run, needs to have a positive Expected Value (+EV).

Expected Value (EV)

This term describes the (long-term) outcome of a specific situation. To calculate the “EV,” you must analyze each possible outcome, multiply it by the probability that each event has of occurring, and then add the results together.
A classic example is that of the die:
Step 1: Analyze the probability of each situation happening:
To draw the number 1, the probability is 1/6
To draw the number 2, the probability is 1/6
… up to number 6.

Step 2: Multiply the values by the corresponding probabilities:
1 * 1/6 = 1/6
2 * 1/6 = 2/6
3 * 1/6 = 3/6
4 * 1/6 = 4/6
5 * 1/6 = 5/6
6 * 1/6 = 6/6

Step 3: Add the probabilities
1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6 = 3,5
In other words, the “expected value” for the launch is 3.5.
Now suppose that a “biased” die is altered, so that Number 1 has a 50% chance of being drawn. Considering that the other numbers have the same chance of being drawn, we obtain:
1 * 50% = 1/2 = 5/10
2 * 10% = 2/10
3 * 10% = 3/10
4 * 10% = 4/10
5 * 10% = 5/10
6 * 10% = 6/10

Note: Logically the sum must be equal to 100%.
Now the expected value has changed. 5/10 + 2/10 + 3/10 + 4/10 + 5/10 + 6/10 = 2.5.

Take advantage of these 5 minutes of study and create your 888 Poker account by clicking this link! You'll get $88 free* and you can also play our weekly $100 freeroll every Tuesday! (*$8 in cash and $80 in bonus).

Now how does this apply to poker? It’s simple… this concept can be applied to considering the chance you have of winning a hand, and it can be the difference between making a correct call or folding.

For example:
Suppose you are in a hand with :Ad :Kd with three other players and the flop comes :3d :6d :Tc . You are the last to act. Player 1 bets and the remaining players 1, 2 and 3 call.

What to do? Call? No, raise!!!
It's easy to understand why. You will complete your flush approximately 35% of the time, with the ace or king being outs. If you raise and the other three players call, you have contributed 25% and have an expected return of 35%. This is clearly a situation where your value, your expected return in the long run, is positive.
After these concepts, we are ready for the main topic.

Mathematical Concepts – Part 2 coming soon…

Adapted Article: Credits to TostesBr