I get a big laugh when I see someone post about how Quick Picks are the greatest. Then they'll post some winning numbers and prizes with a "Look! See!... See! Look!...  Loooook...seeeee." attitude. Well, there are a few problems with comparing Quick Picks to Self Picks (a.k.a. Personal Picks). It has to do with proportionality of work being done. From Powerball's Frequently Asked Questions page, under the heading WHICH HAS THE BETTER CHANCE OF WINNING: COMPUTER PICKS OR PLAYER PICKS? They say, "About 70% to 80% of purchases are computer picks." Computer picks are also know as Quick Picks. This is a fairly good representation of the population as a whole because it's based on actual data obtained on a Nation wide basis without regard to detailed demographics of the purchaser. 70% to 80% is the percentage of the total number of purchased plays, n. n can be any value for any given draw. p, the percentage, is the proportion of n purchases that are Quick Picks. p is represented as a value less than or equal to 1 and greater than or equal to 0, i. e. ( 70% = .70 and 80% = .80). Multiplying p times n gives the number of Quick Pick purchases for that draw, Q_n. The number of Self Picked purchases is just the difference between n and Q_n, S_n = n - Q_n. During any draw there are Quick Pick wins, X, and Self Pick wins, Y. In order to offset the disproportionate number Quick Pick purchases to Self Pick purchases, we need to setup an equation of proportionality that states as Y is to B is the same as X is to A. This satisfies a lead in partial statement of, "All things being equal..." The equation of proportionality is then, Y is to S_n is the same as X is to Q_n becomes (Y / S_n) = (X / Q_n). This allows for a more equal comparison of which type of play has the advantage. We can solve for Y to find by proportion what a Quick Pick equals in terms of a Self Picked purchases based on the approximate percentage of 70% to 80%. As you'll see, the number of purchases becomes immaterial because that value factors out of the final equation.

n - total number of purchases

p - percentage of Quick Pick purchases

Q_n = p · n , Q_n - number of Quick Pick purchases

S_n = n - Q_n , S_n - number of Self Pick purchases

X - Quick Pick wins

Y - Self Pick wins

(Y / S_n) = (X / Q_n), equation of proportionality

Equation of Proportionality Solved for Y

(Y / S_n) = (X / Q_n)

(Y / (n - Q_n)) = (X / Q_n)

(Y / (n - p · n)) = (X / (p · n))

(Y / (n (1 - p))) = (X / (p · n))

Y = ((n (1 - p)) / (p · n)) · X

Y = ((1 - p) / p) · X

Y = ((1 / p) - 1) · X

If we set X = 1, then we can see what one Quick Pick win equals in terms of a Self Pick win.

Y = ((1 / p) - 1) · 1

Y = (1 / p) - 1

Below is a table that shows what a Quick Pick equals for a few different percentages of Quick Pick purchases for any draw. A number less than 1 means the Quick Pick is less than effective as a Self Picked purchase. At 80%, a Quick Pick is only (1 / 4)^th as effective as a Self Picked purchase.

This makes reasonable sense, Quick Picks out weigh the number of Self Picked purchases. This would be like having a football game and on the Quick Pick side you have all 12 players and on the Self Pick side you'd have only about 3 to 5 players. All the players have equal ability. Who do you think is going to win? Really, come on, all things being equal, it's obvious and unfair.

But, you also have to realize, with all those Quick Picks, if they are so great, wouldn't you see more wins per draw?

Self Picked numbers have the edge. Let's look at what 1 Self Picked purchase is equal to in terms of a Quick Pick.

Solving for X instead of Y, we get X = (p · Y) / (1 - p)

Set Y = 1, the equation is X = p / (1 - p)

As you can see, at 80% you'd have to have at least 4 Quick Pick wins in the same draw to be the same as 1 Self Pick win in the same draw.

Quick Picks can't match the power of Self Picks.

Interesting Doug!

I think self picks have the edge too.

Many self-picks are random-picks as are quick-picks, but have the advantage of being edited for duplications, grouping and formation of numbers that players may want to avoid or include on their tickets.

Even when I play randomly picked numbers I like making out my playslips which allows me know what they are before I buy my tickets.

Your thesis is very well written and presented. I too believe that self picked numbers are better than quick picks. And, your post helps to convince me of this belief. Thanks for doing the math and sharing your findings!

Amen ! I have no relationship with any lotto computor so why would the computor do me any favors? I look out for myself and pick my own to control my destiny. Just my opinion.

I appreciate recreational math at least as much as the next guy, but that was a lot of unnecessary math to figure out that if 80% of tickets are QP's there are 4 QP's sold for every self pick sold. Wouldn't it have been a lot simpler to just  divide .80 by .20?

Now, what about the actual data on the number of QP winners vs selfpick winners? The rest of the quote from the powerball site says that about 70 to 80% of the winners are QP's, so their (extensive) data seems to suggest that QP and SP both win in proportion to sales.

It has always been my experience, excellent derivation and conclusion. Thanks Doug.

One of the advantages of picking your own numbers is you can introduce a bias that shouldn't and can't exits with QPs. 

For example, since MegaMillion changed its matrix 231 drawings back the winning combinations have matched 2000 of the 27720 possible combinations of 3's in a pool of 56 numbers.  Each combination of 5 have 10 of them and about 50% of the winning combinations have 10 new ones and 40% have 9 new ones every drawing.  By making sure the combinations you play have as many new combinations of 3's as possible, you increase the odds of at least matching three numbers and hopefully more. 

There may be other bias you've noticed in the winning combinations and by picking your own combinations you can avoid or take advantage of them.

I'd like to say that in no way should Quick Picks be etched of the equation.

However, when someone uses Quick Picks as the banner headline to indirectly put down those who choose their own numbers, well, that's just not right. From my pervious post I stated first, "This makes reasonable sense, Quick Picks out weigh the number of Self Picked purchases. This would be like having a football game and on the Quick Pick side you have all 12 players and on the Self Pick side you'd have only about 3 to 5 players. All the players have equal ability. Who do you think is going to win? Really, come on, all things being equal, it's obvious and unfair." The highlighted portions show that I acknowledge the fact there are is a disproportionate number of winning Quick Picks to Self Picks. From the Powerball FAQ's page, they say "About 70% to 80% of winners are computer picks." Underscore, Obvious and Unfair.

My second posted statement, "But, you also have to realize, with all those Quick Picks, if they are so great, wouldn't you see more wins per draw?", was intended to be a little sarcastic and facetious. Mostly directed toward Jackpot wins, but with the recent multi-Mega Millions winners, maybe they read this. Mwww-ah-ahah, I have more control than they know.

Anyway, the overall objective was to level the unfair playing field that Quick Picks and Self Picks are playing on. Also, there are other aspects of Self Picked number that have an advantage that far out weigh Quick Picks. One of these can be expressed in one word, 'Discretion.' With Quick Picks you have absolutely none. Self Picks give you that leeway to make an Intelligent decision about what numbers you'd like to play. There is no Quick Pick in the world that can even come close to this.

In ending, I'd like to see the Quick Pick believer gather up all those Quick Pick Losers in one place and tell them how they should love their Loosing Quick Picks because they are so great. Please make sure to bring someone else with you and video record this for me.  I've never seen a hoard of disgruntled Quick Pick Losers tear someone limb-from-limb.

If you subscribed to the list of winners e-mail for any given lottery game you might think differently.

I get the one for the Illinois Little Lotto since it's the one I play the most, there's a drawing everyday, and it gets hit pretty often. Most of those hits are quick picks, that's al there is to it. 

Here's August:

 LITTLE LOTTO PRIZE PAYOUTS FOR FRIDAY, AUGUST 03, 2007
 
 
 Winning NUMBERS: 01 - 05 - 26 - 36 - 39
 
 
 PLAYER(S) MATCHING 5 OF 5 NUMBERS
    INCLUDING SUBSCRIPTION WINNERS:        2
 EACH PLAYER WILL RECEIVE:        $190,000.00
 
      Winning TICKET(S) WERE SOLD AT:
 
      828178    CC FOOD MARTS            (QP)
           
 
      258707    SPEEDWAY #5378           (QP)
             

LITTLE LOTTO PRIZE PAYOUTS FOR SUNDAY, AUGUST 05, 2007
 
 
 Winning NUMBERS: 03 - 14 - 25 - 27 - 28
 
 
 PLAYER(S) MATCHING 5 OF 5 NUMBERS
    INCLUDING SUBSCRIPTION WINNERS:        1
 EACH PLAYER WILL RECEIVE:        $150,000.00
 
      WINNING TICKET(S) WERE SOLD AT:
 
      800219    CASEYS GEN STORE #2287
       
LITTLE LOTTO PRIZE PAYOUTS FOR TUESDAY, AUGUST 07, 2007
 
 
 WINNING NUMBERS: 01 - 11 - 14 - 26 - 38
 
 
 PLAYER(S) MATCHING 5 OF 5 NUMBERS
    INCLUDING SUBSCRIPTION WINNERS:        1
 EACH PLAYER WILL RECEIVE:        $175,000.00
 
      WINNING TICKET(S) WERE SOLD AT:
 
      201535    PAYLESS TOBACCO          (QP)
         

LITTLE LOTTO PRIZE PAYOUTS FOR WEDNESDAY, AUGUST 08, 2007
 
 
 WINNING NUMBERS: 06 - 16 - 25 - 34 - 35
 
 
 PLAYER(S) MATCHING 5 OF 5 NUMBERS
    INCLUDING SUBSCRIPTION WINNERS:        1
 EACH PLAYER WILL RECEIVE:        $100,000.00
 
      WINNING TICKET(S) WERE SOLD AT:
 
      095125    GAS PLUS FOOD MART         (QP)
           

etc.... It won't let me post them all because they're in caps and it's too time consuming to make them  enough lower case to post, but for August 11 out of 17 winning tickets were quick picks.  That's a very typical month. 

I buy a quick pick for most every mega draw. I am usually never happy with the numbers on them --- meaning i rarely get quick picks that have numbers i would have even thought of playing. When we bought quick picks in a pool i would go over the numbers and shake my head having found that out of 100 or so tickets many tickets had similar combinations of numbers either sequentially or by position. I expected to see lines that are completely different from one another. Not tickets with the same numbers bunched up.

Of course i realize that every ticket has the same possibility of winning something.

I just wish the numbers on quick picks were more dispersed over the field of numbers. And not the same on every other or several lines.

Sometimes i take the quick pick numbers i get on a group of tickets and fill out tickets with different numbers hoping to edge my selections in my favor. Hasn't worked yet but there always the next draw.    

four4me

But how often are the numbers drawn ones we would have played? Evidently not all that often!

I'd like to add, that in addition to "discretion" there is "intuition".  Human intuition cannot be measured empirically and therefore cannot be discounted as a good resource.

You can analyze, quantify, and calculate with all the tools we have at our disposal, but there is nothing that can match the human brain's ability to assimilate, process, and draw conclusions from any set of data it is given, instantaneously.

 "I think therefore I pick my own........"

Notice the left out information:

1. The total number of Quick Pick purchases it took to get that(those) win(s) for that day's draw.

2. The total number of Quick Pick purchases for the draws spanning 2007-08-03 to 2007-08-08 even when there was no jackpot Quick Pick win.

3. The numerous stores where people bought Losing-jackpot Quick Picks.

And at 70% to 80% of the purchases, I think you can get the picture.