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Calculating odds for a subset of numbers

Topic closed. 11 replies. Last post 5 years ago by time*treat.

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Posted: April 24, 2012, 8:39 pm - IP Logged

Assuming I'm playing 56/46 MegaMillions and I'm able to pick 200,000 tickets for each drawing

that cotains the Jackpot winning ticket for 75% of the drawings. How would I calculate my odds for each drawing?

I've calculated this several different ways and nothing seems right. It's obviously more than 200k/1 but

less than 173m/1.

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    cleveland ohio
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    Posted: April 25, 2012, 9:06 pm - IP Logged

    im probably not understanding the question correctly but youve already given your odds by saying you'll hit 75% of the time. The amount of tickets played becomes moot at that point. If you play only 1 ticket or 10 million tickets each draw if you hit 75% of the time your odds of hitting in any given draw are .75:1

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      Posted: April 26, 2012, 1:30 pm - IP Logged

      I'm not hitting 75% of the time. I'm hitting one time out of a pool of 200K 75% of the time.

       

      I think I'm pharsing it poorly maybe. Let me try to restat it.

       

      Here are the givins:

      1. I create a pool of 200K tickets using my system.

      2. At least one of the tickets in the 200K pool is a jackpot winner in 75% of the drawings.

       

      Overall my odds seem to be 1 in 200K but only 75% of the time. So what I'm asking is how

      do I take the fact that my system is only able to produce a winner in 75% of the drawings

      and apply that to the 200K to 1 odds?

       

      Don't know if that makes it any clearer.

        RJOh's avatar - chipmunk
        mid-Ohio
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        Posted: April 26, 2012, 2:43 pm - IP Logged

        I'm not hitting 75% of the time. I'm hitting one time out of a pool of 200K 75% of the time.

         

        I think I'm pharsing it poorly maybe. Let me try to restat it.

         

        Here are the givins:

        1. I create a pool of 200K tickets using my system.

        2. At least one of the tickets in the 200K pool is a jackpot winner in 75% of the drawings.

         

        Overall my odds seem to be 1 in 200K but only 75% of the time. So what I'm asking is how

        do I take the fact that my system is only able to produce a winner in 75% of the drawings

        and apply that to the 200K to 1 odds?

         

        Don't know if that makes it any clearer.

         tickets or chances per draw  200000
         possible combos of 5/56 + 1/46 numbers = 175711536
         MATCH    ODDS            WINNING COMBOS  ODDS 200000 CHANCES   EXPECT MATCHES
         5/5+B   1 : 175711536      1              1 : 879                     0.00
         5/5+0   1 : 3904701        45             1 : 20                      0.05
         4/5+B   1 : 689065         255            1 : 3                       0.29
         4/5+0   1 : 15313          11475          1 : 0                      13.06
         3/5+B   1 : 13781          12750          1 : 0                      14.51
         3/5+0   1 : 306            573750         1 : 0                     653.06
         2/5+B   1 : 844            208250         1 : 0                     237.04
         1/5+B   1 : 141            1249500        1 : 0                    1422.22
         0/5+B   1 : 75             2349060        1 : 0                    2673.77
         ______________________________________________________________________________
         overall odds are 1 : 39.8            5014.0 total expected wins 

        With a pool of combinations that large, you should expect to win something even if it isn't a jackpot.

         * you don't need to buy more tickets, just buy a winning ticket * 
           
                     Evil Looking       

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          Posted: April 26, 2012, 4:48 pm - IP Logged

          Yes, 879 to 1 makes sense but I'm not playing all 200K numbers(that would be nice though!).

           

          I'm trying to calculate my odds of picking the winner out of the 200K ticket pool if I play X number of tickets and

          I know the pool contains the winner 75% of the time. The odds are 200K to 1 at least if I play a single

          ticket but the part I'm not getting my head around is how the 75% changes things. Does it increrase the

          odds 25%? So instead of 200K to 1 on a single ticket it's now 250K to 1?

           

          What software did you do the odd's calculation with?

            RJOh's avatar - chipmunk
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            Posted: April 26, 2012, 5:26 pm - IP Logged

            Yes, 879 to 1 makes sense but I'm not playing all 200K numbers(that would be nice though!).

             

            I'm trying to calculate my odds of picking the winner out of the 200K ticket pool if I play X number of tickets and

            I know the pool contains the winner 75% of the time. The odds are 200K to 1 at least if I play a single

            ticket but the part I'm not getting my head around is how the 75% changes things. Does it increrase the

            odds 25%? So instead of 200K to 1 on a single ticket it's now 250K to 1?

             

            What software did you do the odd's calculation with?

            You are misreading the odds on that chart.  They are saying the odds of the winning 5+1 combination being among your 200K combinations are 1:879 not 75% and your odds of picking the winning combination from them could be zero.  You made an assumption that the charts shows is not true.  If you physical have 200K combinations, check them again with previous drawings.

            When MM had a jackpot of a half billion dollars, don't you think if players had a 75% chance of winning it with only 200K of tickets there would have been at least 10-50 of them trying it?  After all when Massachusetts had their run down lottery where 300K tickets could win 3-4 millions dollars, it attracted players from Michigan and other places who brought up to 300k of tickets.

            Think of it this way.  If it takes 175 million combinations to have the 5+1 winning combination 100% of the time how can only 200K combinations have the winning 5+1 combinations 75% of the time?

            *I did that chart using the standard probability formula which I found on several websites and divided the results by 200K.  I think there is an odds calculator here at LP.

             * you don't need to buy more tickets, just buy a winning ticket * 
               
                         Evil Looking       

              RJOh's avatar - chipmunk
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              Posted: April 27, 2012, 3:16 pm - IP Logged

                                               CALCULATE ODDS
               combination size             5
               basic pool size              56
               (B) Bonus pool size          46
               smallest match no (B) number 3
               largest match with bonus     5
               smallest match with bonus    0
               tickets or chances per draw  200000
                possible combos of 5/56 + 1/46 numbers = 175711536
               MATCH    ODDS            WINNING COMBOS  ODDS 200000 CHANCES        MATCHES
               5/5+B   1 : 175711536      1              1 : 879                    0.00
               5/5+0   1 : 3904701        45             1 : 20                      0.05
               4/5+B   1 : 689065         255            1 : 3                        0.29
                4/5+0   1 : 15313          11475          13 : 1                     13.06
               3/5+B   1 : 13781          12750          15 : 1                     14.51
                3/5+0   1 : 306            573750         653 : 1                    653.06
               2/5+B   1 : 844            208250         237 : 1                   237.04
               1/5+B   1 : 141            1249500        1422 : 1                 1422.22
               0/5+B   1 : 75             2349060        2674 : 1                 2673.77
               ______________________________________________________________________________
               overall odds 1 : 39.8           5014.0 covered wins of 4405086 possible wins
                4405086  winning combos = 2.5 % of possible combos

               * you don't need to buy more tickets, just buy a winning ticket * 
                 
                           Evil Looking       

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                cleveland ohio
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                Posted: April 28, 2012, 1:48 am - IP Logged

                Yes, 879 to 1 makes sense but I'm not playing all 200K numbers(that would be nice though!).

                 

                I'm trying to calculate my odds of picking the winner out of the 200K ticket pool if I play X number of tickets and

                I know the pool contains the winner 75% of the time. The odds are 200K to 1 at least if I play a single

                ticket but the part I'm not getting my head around is how the 75% changes things. Does it increrase the

                odds 25%? So instead of 200K to 1 on a single ticket it's now 250K to 1?

                 

                What software did you do the odd's calculation with?

                your trying to mix in different equations without a given peramiters. Basic if you played all 200K numbers your odds on any given draw should be 1-250000. Again your trying to mix in 2 totally different related peramiters so Im not even sure if that is right. I just used the 1-200K and added in 25% because that is the miss rate.

                  time*treat's avatar - radar

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                  Posted: April 28, 2012, 2:03 am - IP Logged

                  Assuming I'm playing 56/46 MegaMillions and I'm able to pick 200,000 tickets for each drawing

                  that cotains the Jackpot winning ticket for 75% of the drawings. How would I calculate my odds for each drawing?

                  I've calculated this several different ways and nothing seems right. It's obviously more than 200k/1 but

                  less than 173m/1.

                  Num = Number of tickets you play out of 200,000

                  Set = Set of 200,000 super candidates

                  Pct = Percent of times this super set has jackpot winning combo (0.75 or 75%)

                  Odds = Num * Pct / Set

                  extrema:
                  let Num = 1, then odds of winning a jackpot become 1 in 266,666
                  let Num = 200,000, then odds of winning a jackpot become 1 in 1.333 (three out of four)

                  In neo-conned Amerika, bank robs you.
                  Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.

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                    Posted: April 28, 2012, 5:57 pm - IP Logged

                    You are misreading the odds on that chart.  They are saying the odds of the winning 5+1 combination being among your 200K combinations are 1:879 not 75% and your odds of picking the winning combination from them could be zero.  You made an assumption that the charts shows is not true.  If you physical have 200K combinations, check them again with previous drawings.

                    No, I did not misread the odds, not sure what I posted that made you think I did. 173M / 200K ~= 879. Makes sense as i said(if I were playing all 200K tickets)  but discounts the 25% non hit rate. And the odds are still 200K to 1 AT least since I'm not playing 200K tickets.

                    Think of it this way.  If it takes 175 million combinations to have the 5+1 winning combination 100% of the time how can only 200K combinations have the winning 5+1 combinations 75% of the time?


                    Maybe having the right programer come up with a system that will do just that?



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                      Posted: April 28, 2012, 5:58 pm - IP Logged

                      Pct = Percent of times this super set has jackpot winning combo (0.75 or 75%)

                      Odds = Num * Pct / Set


                      Simple and I think I think these are the right odds.

                       

                      And I think you meant Odds = (Num / Pct ) / Set

                      Or  266666 = (200000/.75) / 1

                      Thanks!

                        time*treat's avatar - radar

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                        Posted: April 28, 2012, 10:59 pm - IP Logged

                        Pct = Percent of times this super set has jackpot winning combo (0.75 or 75%)

                        Odds = Num * Pct / Set


                        Simple and I think I think these are the right odds.

                         

                        And I think you meant Odds = (Num / Pct ) / Set

                        Or  266666 = (200000/.75) / 1

                        Thanks!

                        Ha! Yeah, that. LOL

                        Cheers

                        In neo-conned Amerika, bank robs you.
                        Alcohol, Tobacco, and Firearms should be the name of a convenience store, not a govnoment agency.