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If you had 10 bucks to bet...

Topic closed. 132 replies. Last post 6 years ago by JADELottery.

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What do you think is the better bet?

1 Play / 10 Draws [ 58 ]  [64.44%]
10 Plays / 1 Draw [ 32 ]  [35.56%]
Total Valid Votes [ 90 ]  
Discarded Votes [ 3 ]  
RJOh's avatar - chipmunk
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Posted: April 8, 2011, 8:29 pm - IP Logged

Alright, using your example of hitting a target we’ll setup a simple expression of what we are proving by generalizing a similarity.

First, we have the target shown below. The target is the total possible outcomes for a lottery of N numbers taken R at a time.



Next we have an arrow that represents a selection that is to be made from that total possible set of outcomes. The selection could be a Play or it could be a Draw; either way, they are the same R selections from N numbers.



When it hits the target, it selects an outcome that can be expressed as a smaller area around the arrow shown below. That area represents one of the possible outcomes or the R selections from N pool of numbers.



When two arrows have overlapping areas there is said to be a match between the two selections. The following image shows what this looks like on our target.



We can setup an example of our two different types of strategies of playing 10 bucks. Below are the two different examples.



From those two examples, can you tell me which is which; Either 10 Plays / 1 Draw or 1 Play / 10 Draws?

You could not say exactly which is which based on those hits shown. That’s what the probability, (Q * C(R, M) * C(N – R, R – M)) / C(N, R), is generalizing and it is equally applicable to both examples of 1 Play / 10 Draws and 10 Plays / 1 Draw.

They both look the same because there is one target and 10 arrows in each circle (10 plays per one draw).  If you are representing 10 arrows shot at 10 different targets (one play per draw for 10 draws) then you should have 10 large circles with one target and one arrow in each.  That might be interpreted as hitting the target is more likely if all ten arrows were shot at the same target since it allows more misses of the same target.

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

    JADELottery's avatar - MeAtWork 03.PNG
    The Quantum Master
    West Concord, MN
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    Posted: April 8, 2011, 9:06 pm - IP Logged

    They both look the same because there is one target and 10 arrows in each circle (10 plays per one draw).  If you are representing 10 arrows shot at 10 different targets (one play per draw for 10 draws) then you should have 10 large circles with one target and one arrow in each.  That might be interpreted as hitting the target is more likely if all ten arrows were shot at the same target since it allows more misses of the same target.

    Your statements have many flaws.

     

    They both look the same because there is one target and 10 arrows in each circle (10 plays per one draw).

    Incorrect because the large circle is not a draw, it is the total possible outcomes and each arrow is a selection or sample from those outcomes. The draw is an arrow just like your play is an arrow.

     

    If you are representing 10 arrows shot at 10 different targets (one play per draw for 10 draws) then you should have 10 large circles with one target and one arrow in each.

    A misperception as it relates to the first incorrect assumption. There cannot be more than one target, the target is all the possible combinations that can be selected.

     

    That might be interpreted as hitting the target is more likely if all ten arrows were shot at the same target since it allows more misses of the same target.

    Your conclusion is therefore based on flawed logic and has not established the proper relationship to the 1 Play / 10 Draws and 10 Plays / 1 Draw Probability.

    Presented 'AS IS' and for Entertainment Purposes Only.
    Any gain or loss is your responsibility.
    Use at your own risk.

    Order is a Subset of Chaos
    Knowledge is Beyond Belief
    Wisdom is Not Censored
    Douglas Paul Smallish
    Jehocifer

      RJOh's avatar - chipmunk
      mid-Ohio
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      Posted: April 8, 2011, 9:17 pm - IP Logged

      I'll have to start over and read this thread again and then maybe I'll have a clearer understanding of your graphs.

      RJOh

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


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        Posted: April 9, 2011, 12:28 am - IP Logged

        I'll have to start over and read this thread again and then maybe I'll have a clearer understanding of your graphs.

        RJOh

        RJOh,

        I think I know what might be keeping you from following Doug's logic.  When you think of betting on 10 Draws, 1 Ticket each, you probably subconciously think of time, that the scenario will take 10 days to complete.  On the other hand, when you think of purchasing 10 Tickets for 1 Draw, your mind sees it happening in 1 day.  This can be confusing when trying to equate the two scenarios.

        To make things simpler, because of parimutel complications, let's assume you buy ten unique Tickets for each of the 2 scenarios.  For the 10 Tickets/1 Draw scenario, just imagine buying all 10 Tickets on the same day for one game in one state.  Now you have 10 Tickets with odds for each component as outlined by Doug at the outset.  Now comes the mind trick.  For the 10 Draws/1 Ticket each scenario, just assume you purchase all $1 Tickets in 10 different (5,39) games in 10 different states ON THE SAME DAY!  What are the odds for these 10 Tickets?  The same as the other 10!

        I hope this helps.

        --Jimmy4164


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          Posted: April 9, 2011, 1:04 am - IP Logged

          After much thought I came to the following conclusion, and i'm sticking with it. Unless someone can convince me otherwise, this makes much sense.

          The scenario shows one side having 10 bets in one draw, compared to one bet a draw for 10 consecutive draws. Here's my solution to this.  I think the best way is to use simpler games like the P-3 with a 1000 to 1 odds for a straight bet to better illustrate this.

           I believe that the scenario that involves 10 bets  for one draw seems to be the best one, and I'll explain why.

          If you exaggerate an enigma to a higher degree, sometimes it makes more sense.

          To apply this to the p-3, one must know that it's a 10 to 1 ratio (10 bets or 1 bet)...10 to 1.....

          Let's exaggerate the 10 bets, but nine times it's weight. Now the figure is 90 bets. Let's go one step further and make the nine's weight ten times heavier making it 900.

           The "1" in the 10 to "1" ratio is now  90 bets.

          So now we have a better picture, a more exaggerated picture. Sort of looking at something through a magnifying glass.

          Now ask the same question, but instead of saying 10 bets in a draw, or one bet in each of 10 draws..... You should say.....900 bets in one draw, or 90 bets in ten draws.

          Who in their right mind would choose 90 bets in each of 10 draws?.....RIGHT??????

          Knowing that there would be a very good chance that I'd win that 500 bucks with 900 bets in one draw, Id be a total fool to pick the 90 bets for 10 separate draws....don't you think?

          Please show me the flaw in that logic.

          Everything is still the same except that it's proportionally higher in count. 10 is now 900, and 1 is now 90.

          900 to 90 is the same as 10 to 1.....They're both 10 times higher than the other but the only difference is the story they tell.


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            Posted: April 9, 2011, 1:27 am - IP Logged

            Ran out of time to edit, but I wanted to say that's it not exactly 100% proportional, but close enough. Pretty much a 10 to one ratio compared to a 9 to 1....Just wanted to clear that up....lol 

              ttech10's avatar - blobdude
              Texas
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              Posted: April 9, 2011, 3:40 am - IP Logged

              Ran out of time to edit, but I wanted to say that's it not exactly 100% proportional, but close enough. Pretty much a 10 to one ratio compared to a 9 to 1....Just wanted to clear that up....lol 

              Having not won with ten lines in a draw and not having won with one line in ten draws, I think I would go with ten draws with one draw each. At least that way I still have something to look forward to, rather than having played my ten lines on one draw without winning and continuing with the next nine drawings thinking "what if".

                JADELottery's avatar - MeAtWork 03.PNG
                The Quantum Master
                West Concord, MN
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                Posted: April 9, 2011, 9:03 am - IP Logged

                Ok, let's put it this way.

                Below is an example of the two different playing strategies.

                Can you tell me what example belongs to which strategy?

                 

                02 04 08 15 20
                02 09 22 23 27
                03 12 16 25 30
                01 05 19 23 39
                02 16 22 24 33
                01 03 07 16 32
                08 29 20 35 39
                11 21 26 35 37
                11 12 17 20 23
                04 09 25 28 36
                01 13 16 29 31<- Which is What Strategy? ->02 04 08 15 2001 13 16 29 31
                06 13 18 33 36
                03 06 15 23 26
                07 10 16 24 31
                01 14 18 29 35
                03 06 20 25 31
                08 18 20 33 38
                12 17 23 24 25
                01 07 09 11 19
                01 17 23 25 29

                Presented 'AS IS' and for Entertainment Purposes Only.
                Any gain or loss is your responsibility.
                Use at your own risk.

                Order is a Subset of Chaos
                Knowledge is Beyond Belief
                Wisdom is Not Censored
                Douglas Paul Smallish
                Jehocifer

                  JADELottery's avatar - MeAtWork 03.PNG
                  The Quantum Master
                  West Concord, MN
                  United States
                  Member #21
                  December 7, 2001
                  3675 Posts
                  Online
                  Posted: April 9, 2011, 9:13 am - IP Logged

                  Ok, let's put it this way.

                  Below is an example of the two different playing strategies.

                  Can you tell me what example belongs to which strategy?

                   

                  02 04 08 15 20
                  02 09 22 23 27
                  03 12 16 25 30
                  01 05 19 23 39
                  02 16 22 24 33
                  01 03 07 16 32
                  08 29 20 35 39
                  11 21 26 35 37
                  11 12 17 20 23
                  04 09 25 28 36
                  01 13 16 29 31<- Which is What Strategy? ->02 04 08 15 2001 13 16 29 31
                  06 13 18 33 36
                  03 06 15 23 26
                  07 10 16 24 31
                  01 14 18 29 35
                  03 06 20 25 31
                  08 18 20 33 38
                  12 17 23 24 25
                  01 07 09 11 19
                  01 17 23 25 29

                  How about this?

                   

                  01 13 16 29 3102 04 08 15 20
                  02 09 22 23 27
                  03 12 16 25 30
                  01 05 19 23 39
                  02 16 22 24 33
                  01 03 07 16 32
                  08 29 20 35 39
                  11 21 26 35 37
                  11 12 17 20 23
                  04 09 25 28 36
                  <- Which is What Strategy? ->01 13 16 29 31
                  06 13 18 33 36
                  03 06 15 23 26
                  07 10 16 24 31
                  01 14 18 29 35
                  03 06 20 25 31
                  08 18 20 33 38
                  12 17 23 24 25
                  01 07 09 11 19
                  01 17 23 25 29
                  02 04 08 15 20

                  Presented 'AS IS' and for Entertainment Purposes Only.
                  Any gain or loss is your responsibility.
                  Use at your own risk.

                  Order is a Subset of Chaos
                  Knowledge is Beyond Belief
                  Wisdom is Not Censored
                  Douglas Paul Smallish
                  Jehocifer

                    JADELottery's avatar - MeAtWork 03.PNG
                    The Quantum Master
                    West Concord, MN
                    United States
                    Member #21
                    December 7, 2001
                    3675 Posts
                    Online
                    Posted: April 9, 2011, 9:16 am - IP Logged

                    How about this?

                     

                    01 13 16 29 3102 04 08 15 20
                    02 09 22 23 27
                    03 12 16 25 30
                    01 05 19 23 39
                    02 16 22 24 33
                    01 03 07 16 32
                    08 29 20 35 39
                    11 21 26 35 37
                    11 12 17 20 23
                    04 09 25 28 36
                    <- Which is What Strategy? ->01 13 16 29 31
                    06 13 18 33 36
                    03 06 15 23 26
                    07 10 16 24 31
                    01 14 18 29 35
                    03 06 20 25 31
                    08 18 20 33 38
                    12 17 23 24 25
                    01 07 09 11 19
                    01 17 23 25 29
                    02 04 08 15 20

                    Or this?

                     

                    01 13 16 29 31
                    06 13 18 33 36
                    03 06 15 23 26
                    07 10 16 24 31
                    01 14 18 29 35
                    03 06 20 25 31
                    08 18 20 33 38
                    12 17 23 24 25
                    01 07 09 11 19
                    01 17 23 25 29
                    02 04 08 15 20<- Which is What Strategy? ->01 13 16 29 3102 04 08 15 20
                    02 09 22 23 27
                    03 12 16 25 30
                    01 05 19 23 39
                    02 16 22 24 33
                    01 03 07 16 32
                    08 29 20 35 39
                    11 21 26 35 37
                    11 12 17 20 23
                    04 09 25 28 36

                    Presented 'AS IS' and for Entertainment Purposes Only.
                    Any gain or loss is your responsibility.
                    Use at your own risk.

                    Order is a Subset of Chaos
                    Knowledge is Beyond Belief
                    Wisdom is Not Censored
                    Douglas Paul Smallish
                    Jehocifer

                      RJOh's avatar - chipmunk
                      mid-Ohio
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                      Posted: April 9, 2011, 11:26 am - IP Logged

                      I think I get it now. 

                      Buy one ticket with 10 combinations for 1 draw, you get 10 trys (↓) to match 1 winner (↑)


                        ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓

                                 

                                  ↑

                       

                      Buy one 1 combinations for 10 draws, 10 winners (↑) try to match your 1 combination (↓).


                                 

                       

                        ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑ ↑


                      Both strategies are the same but from opposite directions

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

                        RJOh's avatar - chipmunk
                        mid-Ohio
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                        Posted: April 9, 2011, 11:50 am - IP Logged

                        RJOh,

                        I think I know what might be keeping you from following Doug's logic.  When you think of betting on 10 Draws, 1 Ticket each, you probably subconciously think of time, that the scenario will take 10 days to complete.  On the other hand, when you think of purchasing 10 Tickets for 1 Draw, your mind sees it happening in 1 day.  This can be confusing when trying to equate the two scenarios.

                        To make things simpler, because of parimutel complications, let's assume you buy ten unique Tickets for each of the 2 scenarios.  For the 10 Tickets/1 Draw scenario, just imagine buying all 10 Tickets on the same day for one game in one state.  Now you have 10 Tickets with odds for each component as outlined by Doug at the outset.  Now comes the mind trick.  For the 10 Draws/1 Ticket each scenario, just assume you purchase all $1 Tickets in 10 different (5,39) games in 10 different states ON THE SAME DAY!  What are the odds for these 10 Tickets?  The same as the other 10!

                        I hope this helps.

                        --Jimmy4164

                        For the 10 Draws/1 Ticket each scenario, just assume you purchase all $1 Tickets in 10 different (5,39) games in 10 different states ON THE SAME DAY!  What are the odds for these 10 Tickets?  The same as the other 10!

                        Thanks for your efforts to help me understand Doug's logic but the above scenario wasn't in the question. it was a 10/1 or 1/10 in the same game. I think I understand his logic now.

                        It turns out both scenarios are 10 trys to match a combination but from opposite directions.  In the first the player actively seeks the target with ten trys and in the second the player is the target and he hopes one of the 10 winning numbers finds him.

                        This could cause me to rethink my logic of not playing a set of numbers more than once.

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

                          rdgrnr's avatar - walt
                          Way back up in them dadgum hills, son!
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                          Posted: April 9, 2011, 2:11 pm - IP Logged

                          For the 10 Draws/1 Ticket each scenario, just assume you purchase all $1 Tickets in 10 different (5,39) games in 10 different states ON THE SAME DAY!  What are the odds for these 10 Tickets?  The same as the other 10!

                          Thanks for your efforts to help me understand Doug's logic but the above scenario wasn't in the question. it was a 10/1 or 1/10 in the same game. I think I understand his logic now.

                          It turns out both scenarios are 10 trys to match a combination but from opposite directions.  In the first the player actively seeks the target with ten trys and in the second the player is the target and he hopes one of the 10 winning numbers finds him.

                          This could cause me to rethink my logic of not playing a set of numbers more than once.

                          "This could cause me to rethink my logic of not playing a set of numbers more than once."

                           

                          It could cause me to drink.

                          And for that I'm thankful.


                                                                       
                                               
                                                                   

                           

                           

                           

                           

                                                                                                                             

                          "The only thing necessary for evil to triumph is for good men to do nothing"

                                                                                                                      --Edmund Burke

                           

                           

                            JADELottery's avatar - MeAtWork 03.PNG
                            The Quantum Master
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                            Posted: April 9, 2011, 2:14 pm - IP Logged

                            "This could cause me to rethink my logic of not playing a set of numbers more than once."

                             

                            It could cause me to drink.

                            And for that I'm thankful.

                            I was drinking when I posted the Arrows example.

                            Vodka and Cranberry Juice.

                            Pretty buzzed, too.

                            Presented 'AS IS' and for Entertainment Purposes Only.
                            Any gain or loss is your responsibility.
                            Use at your own risk.

                            Order is a Subset of Chaos
                            Knowledge is Beyond Belief
                            Wisdom is Not Censored
                            Douglas Paul Smallish
                            Jehocifer

                              rdgrnr's avatar - walt
                              Way back up in them dadgum hills, son!
                              United States
                              Member #73904
                              April 28, 2009
                              14903 Posts
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                              Posted: April 9, 2011, 2:16 pm - IP Logged

                              I was drinking when I posted the Arrows example.

                              Vodka and Cranberry Juice.

                              Pretty buzzed, too.

                              LOL, I was drinking heavily reading it.


                                                                           
                                                   
                                                                       

                               

                               

                               

                               

                                                                                                                                 

                              "The only thing necessary for evil to triumph is for good men to do nothing"

                                                                                                                          --Edmund Burke