I think odds often get confused with probability or expected statistical frequency. Normally, when I list an odd in a reduced fractional form I am thinking more along the lines of an immediate probability (expressed as a fraction) for that particular trial. I think many other people inadvertently do this also. When playing 2 different Pick 3 combinations in straight form, the ODDS are 2 in 1000 or 2 to 998, but this often gets written as the fraction 2/1000 or 1/500 when reduced. From the point of view of PROBABILITY, the two fractions are both accurate because:
2 ÷ 1000 = 0.002 as does 1 ÷ 500 = 0.002
But which should make more sense to use? Expressing odds the correct way can be just as deceiving as listing the odds as a “fractional probability”. If I play 250 of the total amount of pick 3 combinations (straight) my “odds” are 250 in 1000 or 250:750, which implies that there are 250 ways I can win and whopping 750 ways I can lose. Doesn’t it seem much more practical to take the odds of 250 in 1000 and express it as a reduced fraction of ¼ to indicated that the probability of winning is .25, ¼, 1 in 4 or 25%.
If I said my “odds” were 1 in 4 or ¼ someone may think that there is only four possible outcomes to the game, there is obviously 1000, but there may as well only be a total of four because I’m playing ¼ the total amount of outcomes and the effects of probability will perform the exact same way whether the game is a true 1 in 4 game or a 250 in 1000 game. Statistical analysis proves that to be true.
Playing two 6/49 combos DOES NOT reduce the total amount of combos from 13,983,816 down to 6,991,908, but expressing the odds of 2 in 13,983,816 as a reduced fraction of 1/6,991,908 is accurate if you look at it with the probability of actually winning in mind:
2 ÷ 13,983,816 = 0.00000014302247684
1 ÷ 6,991,908 = 0.00000014302247684
I have enough knowledge of how probability actually works to understand that playing two 6/49 combos is parallel to playing only one combo for a game with 6,991,908 total outcomes. In the same way, if you break down all the Pick 4 numbers into groups of ten you will have 1000 groups that statistically perform and follow the exact probabilities for a 1 in 1000 game like pick 3.