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# The wizard of odds

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In every numeric lottery its numbers are supposed to be drawn at certain frequency rate which is defined as odds for the number. Pick 3 is such a lottery which defines odds for each of its numbers. These are mathematical odds, a ratio that is equal for all numbers.

For Pick 3 lottery there are 3 numbers from 0 to 9 drawn independently to form a 3-digit winning number (e.g. 123). The odds for each of these single digit numbers are the same: 1 in 10.

Thus, if we consider 30 draw span in a lottery there are 90 single-digit numbers drawn in that time. If we apply mathematical odds to all the Pick 3 available numbers (10 of them) in 30 draws each number should be drawn 9 times. Compare this with the frequency chart for 30 draws in June 2012 in Kansas Pick 3 lottery:

0 - 14

1 - 10

2 - 4

3 - 8

4 - 10

5 - 8

6 - 13

7 - 4

8 - 7

9 - 12

Total is 90 as expected. But look at the distribution - not a single number was drawn at its mathematical odds. The difference between the highest and the lowest is 10, the highest was drawn over 3 times more than the lowest. What happened to the mathematical odds, why all the numbers aren't at 9 times frequency as they are supposed to be?

Because there is a feature called the CURRENT ODDS - the odds at which each individual number is drawn at current time. Current odds are independent from the mathematical odds and, while mathematical odds always remain the same, the current ones constantly fluctuate. By using appropriate statistics these odds can be identified and applied to selecting numbers for actual playing.

There is evidence that the current odds for each number do exist and they may sinificantly affect the results of playing. Here is the proof.

Kansas Pick 3 lottery, the month of June 2012, 30 draws. I picked this month without any bias or prejudice - it is the latest data I have available for the whole month at the time of writing (July 20/12).

I compared (backtracked) 2 selection methods for this period of time. I used box play for singles and selected in each case 8 numbers wheeled into 56 combinations. Doubles were ignored.

The methods selected for comparison were hot numbers (the most frequent) for the latest 30 draws and cold numbers (the least frequent), also for the latest 30 draws.

With each draw the frequency charts for hot and cold numbers were updated to make sure their hot or cold status was current.

Both methods always used 8 numbers out of available 10, so there was always a significant overlap. In fact, for hot numbers only 2 coldest would not make the list, and for the cold - only 2 hottest would not fit. 2 out of 10 does not seem to make a significant difference, does it? Well, look at the results.

30 plays in June:

Hot numbers won 16 times.

Cold numbers won 10 times.

For curiosity I also computed stats for overdue numbers (the ones that have been waiting the longest for being drawn) - they won only 8 times.

These results were computed automatically by backtracks. Once I set calculation parameters, the computations were done automatically and no adjustment could be made to affect the results.

The difference between hot and cold numbers is 6 wins. For box single play this means 6 times \$80 = \$480 diference in just one month. For me it's a fair chunk of money. In fact, this may make you earn or loose money in actual playing.

So, how come hots and colds did not score the same within the same time period, while always differing by only 2 numbers? Why such a difference in winning ratio? Because their CURRENT ODDS were not the same. The odds for the hots were always higher than for the colds and this showed in the final results. This proves that considering the current odds for all numbers must be an essential part of selecting numbers for actual playing.

As this analysis illustrates ignoring the current odds for Pick 3 lottery numbers is a prescription for a financial disaster and is most likely the reason why so many people win little or not at all in Pick 3. No matter how you play you always have to have the right numbers to win. And only the current odds will tell you which numbers are right. Mathematical odds should only be used as a reference and never applied to actual number selection.

Entry #7