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The ShOcKiNg truth about powerball odds...

Published:

Last Edited: February 2, 2007, 8:32 pm

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 =

1:17,532,955,440

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.

 

Entry #118

Comments

1.
ayenowitallComment by ayenowitall - February 3, 2007, 9:51 am
Interesting analysis, but you're confusing combinations (combos) and permutations. There are 720 Pick 3 permutations with no doubles or triples, but there are only 120 six-way combinations with no doubles or triples. Divide your 720 by the 6 (1x2x3=6) that you should be using in your example and you'll get that 120 number of combos. By extension, divide that 17,532,955,440 (permutatations) by the 120 (1x2x3x4x5=120) that you should be using in your PowerBall odds calculations and you'll get, 146,107,962 (combinations)... the TRUE odds.
2.
ayenowitallComment by ayenowitall - February 3, 2007, 10:05 am
Actually, that 120 comes from 1x2x3x4x5x1=120. I almost forgot about the red PowerBall 1/42.
3.
hypersoniqComment by hypersoniq - February 3, 2007, 11:26 am
not confusing them at all. the 120 combos are only of interest to box players. in the list of 720 numbers, 5-4-9 only appears once. sure it shows up as 4-9-5, 4-5-9, 5-4-9, 5-9-4, 9-4-5 and 9-5-4... but if you're playing straight, only the 5-4-9 matters in this case.
In a "Sort Order" system, you make reductions based on assuming you are safely eliminating numbers... but in a draw order system, let's assume you picked
25-14-31-16-51
sure that could come out as 14-16-25-31-51 and you would still win, but that wasn't your exact pick.
the thing I confused was the terminology.
If your system picks 12 as the first number drawn and it was the fourth number drawn, you were wrong... that's just coincidence.

I'm not even working on the white balls right now. The way I see it, if I can't get a handle on the 1:42 red ball, there's no point in moving forward. Right now I'm stuck on basic direction. My goal for phase one is to be able to accurately predict whether the next powerball will be higher or lower (or repeat). I missed the 14's repeat. things are definitely off to a slow start.
4.
ayenowitallComment by ayenowitall - February 3, 2007, 12:29 pm
If that's the way you choose to look at it, more power to you.
Good luck. I hope you can master the red ball selection.
BTW, I cashed a ticket on that 14 red ball repeating last draw, but I also had four other red balls that were wrong. I don't believe it's really possible to predict the draw numbers. All we can do is play smart and respect the odds, whatever we might believe them to be.
5.
hypersoniqComment by hypersoniq - February 4, 2007, 11:16 am
Prediction is off in the future, right now I am after just guessing the direction.
based on the stats I have, 37 was higher than 14, but the confidence index was only 51%
for the next draw, there is an 80% chance that the PB will be lower and draw history confirms that...
what it means now is that I will have to venture a guess (just like every system requires) and assume I can safely eliminate 38,39,40,41,42 from my choices. 37 repeated once in it's 34 appearances, so I can safely drop that one (or so I guess, I was wrong on the 14, but 14 does have 3 repeats)
you always have to assume something, so IF I'm right about the direction, my odds for wed. will be effectively 1:36
see what I'm getting at?
21 of the last 34 appearances of #37 were odd. If I choose to assume the almost 2:1 rate, I can effectively reduce to 1:18
23 of the followers fell in the ranges of 13-30, that leaves
13,15,17,19,21,23,25,27,29 ... I'm now down to 1:9
of those, the highest frequency is 29 (appeared 3 times after the 37)
I'll fill out the bet slip with QP for the white balls and 29 for the PB.

My actual odds are still 1:42
my effective odds based on assumptions is 1:9
of those 9, I picked to go with the most frequent

It's not perfect, but it's a start... you were here for the first live firing of the "system" #29 is my first pick from it...
6.
hypersoniqComment by hypersoniq - February 8, 2007, 5:45 am
well at least the direction was right :-)

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