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Average Losses for Lottery Numbers in Total Drawings, House Advantage, Edge

By Ion Saliu, Founder of Lottery Mathematics

Playing random lottery numbers or favorite numbers guarantees substantial loss in many drawings.

The average loss, in lottery and casino gambling alike, is determined by multiplying the total cost by the house advantage (HA or house edge).

The cost consists of number of tickets played multiplied by the price per ticket.

To calculate the house advantage (HA), we apply this simple formula based on units paid UP over total possibilities TP:

HA = 1 (UP / TP)
(always expressed as a percentage)

For example, in the pick 3 game, they pay 500 units (e.g. dollars) for a straight win. Total straight sets (possibilities): 1000. HA = 1 (UP / TP) = HA = 1 (500 / 1000) = 50%. That's humongous! It's about 10 times worse than what the player faces in American roulette: 5.26%.

If one played 10,000 dollars (one pick-3 number in 10,000 lottery drawings), the average loss would amount to 5000 dollars. If playing, randomly, one pick 3 straight set in 100,000 lottery drawings, virtually every number (straight set) will end up very close to a 50,000-dollar loss.

I doubt there are 100,000 lottery drawings in any state lottery. But we can reduce to scale. Instead of 3 digits, we look at data for one digit only; e.g. the digit in the 1st position. In other words, we derived a new game, a pick 1 lottery game. Total possibilities are now 10. To maintain the same HA, we assume the house pays 5 units per win.

The data available for this game analysis is huge now: over 9000 drawings in my database (in Pennsylvania State Lottery). I run my one-of-a-kind statistical software known as Frequency Rank. I am interested only in the positional frequency, as this hypothetical game has only 1 digit. Here is the report:

         The Pick-3 Digits Ranked by Frequency - By Position
         File: PA-3
         Drawings Analyzed: 9000 | Date: 08-03-2017
         Frequency norm based on probability: 10%

    Rank |    Position 1     |    Position 2     |    Position 3     |
         | Digit  Hits   %   | Digit  Hits   %   | Digit  Hits   %   |

      1  |   7   961  10.68% |   5   931  10.34% |   6   940  10.44% |
      2  |   4   949  10.54% |   1   924  10.27% |   7   927  10.30% |
      3  |   2   938  10.42% |   8   913  10.14% |   5   925  10.28% |
      4  |   0   926  10.29% |   0   897   9.97% |   0   908  10.09% |
      5  |   3   884   9.82% |   9   896   9.96% |   1   897   9.97% |
      6  |   5   883   9.81% |   3   895   9.94% |   8   895   9.94% |
      7  |   6   872   9.69% |   6   895   9.94% |   3   883   9.81% |
      8  |   1   872   9.69% |   4   888   9.87% |   9   883   9.81% |
      9  |   8   869   9.66% |   7   885   9.83% |   2   878   9.76% |
     10  |   9   846   9.40% |   2   876   9.73% |   4   864   9.60% |

You notice, every digit appeared with a frequency very close to the norm: 1/10 or 10%. A few numbers came out with a little better frequency, while others performed just below par. Each and every digit, however, ended up a loser money-wise.

Looking at the digits in the first position, the digit 7 was the best performer with 961 wins. Total winnings: 961 * 5 = 4805. Loss: 9000 4805 = 4195. The digit 9 was the worst performer: 846 wins. Total winnings: 846 * 5 = 4230. Loss: 9000 4230 = 4770.

You saw in the roulette report that some of the numbers ended up as winners (in the straight-up bet). No doubt, I exposed that the particular roulette wheel in the Hamburg Casino was seriously biased (they replaced it later). The lottery drawing machines are less prone to bias, as they are not nearly as complicated mechanisms as the roulette wheels.

We saw that also the lottery machines "favored" some digits over others. There are a few percentages above the norm for some digits. The norm calculates that each digit (in this pick-1 game) should hit 900 times in 9000 "drawings". The best performer, the digit 7 came out by 961 / 900 = 6.8% better than the norm. That "percentage advantage" is still a far cry from the house advantage of 50%. Meanwhile, a 6.8% bias in roulette does beat the HA of 2.7 or 5.3%!

The degree of certainty is very high that the numbers will come out with different frequencies. There will always be discrepancies measured in percentages. In games like roulette, some discrepancy percentages will be high enough to make a profit for the gambler who played those particular numbers. In lottery, however, that phenomenon will never occur. The positive discrepancies always come in small percentages; the house edge is always too high. The greedy lottery commissions could cut down the house edge to 25% and they would still make an indecent amount of money!

The results above were computed for one ticket play. Adding more lottery tickets adds to the cost and total loss. Again, in roulette, playing more numbers can still make a profit for the gambler.

The best lottery software covers 5, 6, 7-number lotto jackpot games.

Ion Saliu's Theory of Probability Book founded on mathematics applied to strategy, systems for lottery, pick-3-4-5 lotteries. Read Ion Saliu's book: Probability Theory, Live!
~ Founded on mathematical discoveries, also applied to creating strategy, systems in lottery software, lotto jackpot games.

Losing big money in lottery is guaranteed if playing randomly without systems.

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Losses amount to thousands of dollars in a lifetime for just one lottery game like pick-3.

Forget about playing random lottery numbers or favorites: You are going to lose a lot.


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