Before moving in a positive direction with my excel work against the PB, I gotta let out the negativity, so here goes...
First, let's start on the same page, with the simplest of all games (nice round numbers), the straight pick 3. (not worth the time to get into box play)
In pick 3, you are playing 3 sequential games of 1:10, you MUST match all 3 games correctly to have a straight hit.
odds of first correct ball = 1:10
odds of also selecting the second correct ball = 1:100 (or 10 possible first game combos times 10 possible second game combos)
odds of ALSO selecting the third correct ball = 1:1,000 (10x10x10)
the range is 0-9 for each game, 000 to 999 for the entire process. To further prove the math I'm about to lay down, most serious pick 3 players know there are 720 combos that contain NO doubles or triples... the derivation is to imagine 10 balls and they pick 3 of them
first ball 1:10
2nd ball 1:9 (one ball is gone)
3rd ball 1:8 (two balls are gone)
10 x 9 = 90, 90 * 8 = 720
All in agreement so far?
now let's look at what the MUSL advertises as the odds for a powerball jackpot win... 1:146,107,962 ... and it's flat out wrong. False on purpose? who knows. NOW let's do the actual math...
the game starts with one group of 55 white balls and one group of 42 red balls. the odds of matching the first number...
1:55 simple enough. on to two numbers
55x54= 1:2,970 (55 for the first ball, then 54 remain)
three numbers (a prize they claim has odds of 1:290) 55x54x53 = 1:157,410
four numbers (they say 1:14,254 ... I say) 55x54x53x52 = 1:8,185,320
five numbers 55x54x53x52x51 = 1:417,451,320 (wait, it gets better...)
odds of winning the powerball jackpot, 55x54x53x52x51x42 =
you read correctly, that is 17 BILLION to one!!! Makes that 15 million minimum look a bit low, yes?
you may slice/dice/analyze this as you see fit... but it's true.
you start with 55 balls, the first one could be any of the 55... the second could be any of the 54 remaining...
This is what we're all up against.... and I STILL accept the challenge!
the bright side is the 42:1 odds of matching a red ball... that is where I choose to begin anew. Also, all 17 billion are not unique, many sets contain the same numbers. BUT trying to create a system that uses draw order data does require you realize the TRUE odds.