## Philippine Lotto Probability – How to do the Calculations

Posted: May 21, 2008 in Lotto and Swertres Tips
Tags: , , , , ,

To truly understand how Philippine Lotto odds are calculated we first need to understand basic law of probability. Probability is important because it tells us how many times a particular number or combination of numbers should occur over time.

To simplify this example we will use a single dice cube as an example.
If you were to roll a dice what would be the chances of rolling, say a two? Because there are 6 possible numbers that could be rolled on the single dice and since only one of them can appear on a single roll then you have 1 chance in 6 (1/6). Pretty easy so far!

Now lets work out the odds of a combination of different numbers occurring?
What would be the chances of rolling a two or a six? In this case the chances of rolling a two are 1/6 and the chances of rolling a six are 1/6. Therefore you simply ADD the two outcomes: 1/6 + 1/6 = 2/6 or 1/3. Therefore the chances are 1 in 3 of rolling either a 3 or 6. Still pretty simple.

What would be the odds of rolling a two on two consecutive rolls of the dice? In this case the odds are MULTIPLIED together. Thus we have 1/6 × 1/6 = 1/36. Thus the chances of rolling a two on 2 consecutive rolls is 1 chance in 36.

Ok, So how does this work with lotto?
The calculations are the same; we simply expand the above theory.
If we select 6 numbers and the game has 50 numbers in the pool the odds are calculated as follows.

* The odds of having the first number drawn are simply 6 in 50 (6/50).

* Since we have already picked one of our six numbers and there is one less number in the pool that can be picked, then there are only five of a possible 49 numbers left in the pool that can be drawn. Therefore the odds of having the second number drawn is 5 in 49 (5/49).

* Since we now have four of our six picks left and there are now only 48 balls left in the pool to be drawn, the chances of getting the third is 4 in 48 (4/48).

* We now have three of our six picks left and only 47 balls left in the pool to be drawn. Therefore the chances of getting the forth number is 3 in 47 (3/47).

* With two of our six picks left and only 46 balls left in the pool. The chances of getting the fifth number are 2 in 46 (2/46).

* With only one of our six picks left and only 45 balls left in the pool, the chances of getting the last number is 1 in 45 (1/45).

To calculate the odds of picking all six numbers we multiply the individual odds together to get the overall odds: 6/50 × 5/49 × 4/48 × 3/47 × 2/46 × 1/45 = 720/11,441,304,000 or 1/15890700 (1 chance in 15.89 million).

The standard formula used to calculate odds is as follows:
Odds = Fac(x) ÷ [Fac(n) × Fac(x – n)].
What the variables mean are;
* Fac( ) means factorial, which means multiplying a number out by all of its factors. For example Fac(6) would be 6 x 5 x 4 × 3 × 2 × 1 = 720
* x = the number of balls in the game pool (in the above example, 50).
* n = the numbers allowed to be chosen (in above example, 6).
Thus in a 6/50 lotto the odds as follows:
Odds = Fac(50) ÷ [ Fac(6) × Fac(50-6)] = 1/15,890,700: the same as the long hand calculation performed above.

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