my last paragraph is straightforward.... powerball is 2 games, a 5 of 53 and then a 1 of 42... by buying 42 tickets, each with a diffferent powerball number, you have beat the second of 2 games... but not at a cost-effective return... ($3 for a $42 investment)
what I am trying to say is that you have no control over the possible outcomes, nothing you can do will change th fact that 1,000 possibilities exist for the pick 3... you only have control of the number of FAVORABLE outcomes...
by buying more than one ticket for one single draw, you increase the number of favorable outcomes, but there is nothing you can do to reduce the number of possible outcomes...
the odds "reduction" in my last paragraph simply eliminates the combined odds, by covering all 42 powerballs you are left with just the 5/53 game. which has posted odds at the powerball site.
One of the reasons I don't go with the flow on this is the blatant misleading advertising on the PA lottery website... in the Match6 and the old super6, they took the actual odds and divided them by 3 just because they give you 2 quick picks... look at the odds posted for match6 then look at any other state's 6/49 odds... (I'm not referring to the secondary game, where you can match numbers on all 3 lines) .... where did 2/3 of the possible outcomes go? The answer? nowhere... to get the odds as posted by the PA lottery for the match6, simply multiply by 3... that's how many possible combinations truly exist.
I agree that if you buy 10 tickets for a 1:42,000,000 game that your ratio of favorable outcomes to possible outcomes is then 10:42,000,000... I do NO agree with the reduction to 1:4,200,000... it is still just one dvent and there are still 42,000,000 possible outcomes... I used to believe the expression could be reduced, it does sound much more promising that way... but in reality, you only have control over the favorable outcomes... there is nothing you can do to change the possible outcomes portion of the expression... they probably should have expressed it in another form, because we're all taught to simplify expressions from an early age.
In most cases the only harm in reducing the expression is lulling yourself with false hope... but in other cases, like the PA lottery, it's just plain wrong.