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Probabilty of Someone Winning a PB & MM Jackpot in the same Week!

Topic closed. 63 replies. Last post 10 years ago by Stack47.

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twisted's avatar - underground
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Posted: March 4, 2007, 3:26 pm - IP Logged

Totally disagree, John.  Why do you think the odds would be cut in half?  That would mean that everyone will eventually win if they just keep playing! 

The odds are the odds are the odds are the odds.  They don't change just because there is one drawing, two drawings or 10 drawings.  This is the same logic people use when they assume buying 2 tickets changes the odds. It does very slightly, but not by 50%.  If the odds are 1 in 10 million, 2 tickets makes the odds 2 in 10 million, not 1 in 5 million.  There is a difference.

The chance of an individual winning both the MM and the PB in his lifetime (not just in a week) is so atronomical that nobody should even try to imagine it. I'm not saying it can't be done, however, these are 2 entirely different games and winning one doesn't have any effect whatsoever on the odds of winning the other.

If someone buys $87,855,768 (half of the combinations) worth of Mega Millions tickets, while making sure they all have different combinations, their odds of winning are brought down to 1 in 2 (87,855,768 in 175,711,536) or they have a 50% (87,855,768 divided by 175,711,536) chance of winning.  If they still dont have the winning combination, they would loose A LOT of money. 

Ofcourse this is only a hypothetical situation.  No one person will ever buy $87,855,768 of tickets.  They probably couldn't even if they wanted to because I dont think they will be able to buy so many combinations in such a short amout of time you have between each drawings.

So what John and KYFloyd have been explaining is exactly right.  I think the terminology is what is confusing you guys. 

    justxploring's avatar - villiarna
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    Yes, you make sense.  But you are proving my point.  You can't possibly be cutting the odds in half by buying 2 tickets for MM.  Seriously, once I had a discussion about grammar with a boss when I refused to type a letter the wrong way.  I faxed it to Harvard (this is a true story) and it was presented to the English Literature department.  I got a response, which was very surprising.  I was correct. So maybe I'll send a letter to M.I.T.

    In this case I am not 100% sure I am correct.  However, I'm thrilled that Coin Toss and I are on the same page, since I began to doubt my logic.  So far nobody has convinced me I am wrong since it doesn't make sense.  I mean, take the old "odds of being hit by lightning" example.  If a man is standing in his yard, there is a possibility that lighting will strike (odds vary by area, weather and other factors of course) So now his neighbor comes over to chat.  You have 2 men (or tickets) standing in the same place.  Does it now double the chances that lighting will strike? Does it cut the odds in half when one of them walks away?  No.  That's because the possibility that lightning will strike is not related to the men standing there.  The odds of winning a MM or PB game are set odds.  If a game has odds of 1 in 140M, then every time a person buys another ticket, the possibility of winning is increased by 1 for that player, not 100%, the same as the odds aren't reduced by 50% if he only buys 1 ticket.

    As JAG already wrote, this is going nowhere. 

      twisted's avatar - underground
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      Posted: March 4, 2007, 4:02 pm - IP Logged

      Yes, you make sense.  But you are proving my point.  You can't possibly be cutting the odds in half by buying 2 tickets for MM.  Seriously, once I had a discussion about grammar with a boss when I refused to type a letter the wrong way.  I faxed it to Harvard (this is a true story) and it was presented to the English Literature department.  I got a response, which was very surprising.  I was correct. So maybe I'll send a letter to M.I.T.

      In this case I am not 100% sure I am correct.  However, I'm thrilled that Coin Toss and I are on the same page, since I began to doubt my logic.  So far nobody has convinced me I am wrong since it doesn't make sense.  I mean, take the old "odds of being hit by lightning" example.  If a man is standing in his yard, there is a possibility that lighting will strike (odds vary by area, weather and other factors of course) So now his neighbor comes over to chat.  You have 2 men (or tickets) standing in the same place.  Does it now double the chances that lighting will strike? Does it cut the odds in half when one of them walks away?  No.  That's because the possibility that lightning will strike is not related to the men standing there.  The odds of winning a MM or PB game are set odds.  If a game has odds of 1 in 140M, then every time a person buys another ticket, the possibility of winning is increased by 1 for that player, not 100%, the same as the odds aren't reduced by 50% if he only buys 1 ticket.

      As JAG already wrote, this is going nowhere. 

      I'm only saying what KYfloyd and John said but a little differently.  The odds are listed as 1 in 175,711,536.  If you buy 2 tickets, the odds are 2 in 175,711,536.  But the odds are always listed as 1 in something.  So what would 2 in 175,711,536 be in terms of 1 in ???.  Its the same as 1 in 87,855,768.  If someone buys $87,855,768 worth of tickets while making sure they are all different combinations, their odds are 87,855,768 in 175,711,536.  But what is that in terms of 1 in ???.  Its 1 in 2.  So when you need to find any odds in terms of 1 in ???, you just divide the total combinations by how many tickets you buy. 

      Again, I think what is confusing you is the terminology.  If you buy 2 tickets, you only have 2 possibilities in 175,711,536 of winning.  Its a little hard to comprehand but its the same as 1 in 87,855,768 odds of winning.  So it seems that the odds are drastically reduced when you buy 1 more ticket.  But the reality is that we are so numb by hearing numbers like 1 in 175,711,536 that we forget that 1 in 100 are still long odds.

      You can send your quesitons to M.I.T or your state lottery headquarters.  You will get the same answer.

        twisted's avatar - underground
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        Posted: March 4, 2007, 4:12 pm - IP Logged

        Yes, you make sense.  But you are proving my point.  You can't possibly be cutting the odds in half by buying 2 tickets for MM.  Seriously, once I had a discussion about grammar with a boss when I refused to type a letter the wrong way.  I faxed it to Harvard (this is a true story) and it was presented to the English Literature department.  I got a response, which was very surprising.  I was correct. So maybe I'll send a letter to M.I.T.

        In this case I am not 100% sure I am correct.  However, I'm thrilled that Coin Toss and I are on the same page, since I began to doubt my logic.  So far nobody has convinced me I am wrong since it doesn't make sense.  I mean, take the old "odds of being hit by lightning" example.  If a man is standing in his yard, there is a possibility that lighting will strike (odds vary by area, weather and other factors of course) So now his neighbor comes over to chat.  You have 2 men (or tickets) standing in the same place.  Does it now double the chances that lighting will strike? Does it cut the odds in half when one of them walks away?  No.  That's because the possibility that lightning will strike is not related to the men standing there.  The odds of winning a MM or PB game are set odds.  If a game has odds of 1 in 140M, then every time a person buys another ticket, the possibility of winning is increased by 1 for that player, not 100%, the same as the odds aren't reduced by 50% if he only buys 1 ticket.

        As JAG already wrote, this is going nowhere. 

        Lets take your example of 1 in 140M.  Sure when everytime a person buys another ticket, the POSSIBILITY (Not odds) of winning is increased by 1 for that player.  But lets say 70M people buy one ticket, each with a different combination, then the odds of the lottery being(or someone winning) hit is 1 in 2 or 50%.    ODDS are different then POSSIBILITES.  I think thats whats confusing you.  I dont know how better to explain it.  I'm not a very articulate person.

          justxploring's avatar - villiarna
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          Posted: March 4, 2007, 5:09 pm - IP Logged

            But lets say 70M people buy one ticket, each with a different combination, then the odds of the lottery being(or someone winning) hit is 1 in 2 or 50%.   

           

          Twisted - you are correct!  But you are also agreeing with me, but don't seem to realize it.  Yes, buying 70 million tickets is the same as reducing the odds by 50%, which is exactly what I wrote. So why are you saying I'm wrong and confused?

          Don't worry about being articulate.  I think you write very well.  I'm just not sure you are reading all of the posts clearly and seeing what I wrote vs the other people who disagree with me.  In fact, in one of my previous posts I wrote that buying 70 million tickets would cut the odds in half, just as you are saying.  KY Floyd and John both said that buying just 1 more ticket cuts the odds in half.  So you can't be agreeing with all of us!  I also know that possibilities are different than odds.  But the subject matter of this thread using the word probability which is usually considered to be synonymous with "odds"

          Anyway, I don't need to have the last word, and as I said before, I'm no math genius, but I don't think in any way, shape or form, the odds are cut in half when you have a 1 in 140M shot at winning just by purchasing a second ticket, which is what John and KY Floyd are insisting. 

            twisted's avatar - underground
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            Posted: March 4, 2007, 5:27 pm - IP Logged

              But lets say 70M people buy one ticket, each with a different combination, then the odds of the lottery being(or someone winning) hit is 1 in 2 or 50%.   

             

            Twisted - you are correct!  But you are also agreeing with me, but don't seem to realize it.  Yes, buying 70 million tickets is the same as reducing the odds by 50%, which is exactly what I wrote. So why are you saying I'm wrong and confused?

            Don't worry about being articulate.  I think you write very well.  I'm just not sure you are reading all of the posts clearly and seeing what I wrote vs the other people who disagree with me.  In fact, in one of my previous posts I wrote that buying 70 million tickets would cut the odds in half, just as you are saying.  KY Floyd and John both said that buying just 1 more ticket cuts the odds in half.  So you can't be agreeing with all of us!  I also know that possibilities are different than odds.  But the subject matter of this thread using the word probability which is usually considered to be synonymous with "odds"

            Anyway, I don't need to have the last word, and as I said before, I'm no math genius, but I don't think in any way, shape or form, the odds are cut in half when you have a 1 in 140M shot at winning just by purchasing a second ticket, which is what John and KY Floyd are insisting. 

            I think JAG might be right.  This is not going anywhere.  But what I've said so far doesnt agree with what you've said justxploring.  What I've said so far proves that when you buy 2 tickets the odds are 1 in 87,855,769.  If you buy 3 the odds are 1 in 58,570,513.  As you keep on adding 1 more ticket the odds decrease by a smaller number.  If someone was to buy 1,000,000 different combinations, the odds will be approximately 1 in 176 (175,711,536 divided by 1,000,000).

            Sure if you by 2 tickets, the PROBABILITY of you winning is 2 in 175,711,536(meaning there are 175,711,534 combinations remaining).  But in terms of odds that is 1 in 87,855,769.

            If you still dont get it.  I give up.  Hopefully a professor at M.I.T will do a better job explaining when you send your questions. 

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              Posted: March 4, 2007, 6:13 pm - IP Logged

              JAG331

              I had twenty years of casino work and most of the old time bosses said they'd rather have someone who just got a degree in probabilities buy in on one of their games than any other player. 

              Well, I don't have a degree in probabilities....but that's an interesting point.

              Do you think that people who play the probabilities are more conservative with their money?  Or rely less on gut feel or intuition and more on what cards have played (using blackjack as an example)?

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                Posted: March 4, 2007, 6:35 pm - IP Logged

                Here's the formula for what percentage each additional ticket (beyond the first) reduces the odds:

                Nx = x-1

                N stands for the sequence of tickets.  X stands for the particular ticket purchased.

                Here is the second ticket in action:

                 

                N2 = 2-1  = 1/2

                 

                Odds are reduced by one half when you buy the second ticket.

                 

                N21 = 21-1  = 1/21

                 

                Odds are reduced by one twenty-first when you buy the twenty-first ticket, instead of buying only twenty.

                 

                Here's the supporting math.  There are 100 possible combinations in the game.  You buy 20 distinct tickets, odds are 1 in 5.  If you had bought 21 tickets the odds would be 1 in 4.7619.  The odds have been reduced by 4.762% (Yes, the new odds and the percent decrease will always match).  4.7619% is equal to 1/21st.

                  Coin Toss's avatar - shape barbed.jpg
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                  Posted: March 4, 2007, 7:25 pm - IP Logged

                  Here's the formula for what percentage each additional ticket (beyond the first) reduces the odds:

                  Nx = x-1

                  N stands for the sequence of tickets.  X stands for the particular ticket purchased.

                  Here is the second ticket in action:

                   

                  N2 = 2-1  = 1/2

                   

                  Odds are reduced by one half when you buy the second ticket.

                   

                  N21 = 21-1  = 1/21

                   

                  Odds are reduced by one twenty-first when you buy the twenty-first ticket, instead of buying only twenty.

                   

                  Here's the supporting math.  There are 100 possible combinations in the game.  You buy 20 distinct tickets, odds are 1 in 5.  If you had bought 21 tickets the odds would be 1 in 4.7619.  The odds have been reduced by 4.762% (Yes, the new odds and the percent decrease will always match).  4.7619% is equal to 1/21st.

                  Percentages are not odds. Percentage, known in the gambling business as "the  per", is the house pc on any given game or bet.

                  The lowest possible pc the player can go up against is a full odds bet on the Pass or Don't Pass on a crap table (or Come and Don't Come bet odds) - these are the only bets in the entire universe of legal gambling that pay true odds - and people still get slaughtered making these bets, but I digress... 

                  On the game of roulette, except for a couple of bets, the house pc is 5.26% no matter what you bet, whether it's a number stright up (by itself) or "starring a number" getting at it every way possible.  

                  The odds against hitting one number are 37 to 1 (1 number of 38 numbers, American roulette, 1-36, 0 and 00), the house percentage is 5.26%.

                  Those who run the lotteries love it when players look for consistency in something that's designed not to have any.

                  Lep

                  There is one and only one 'proven' system, and that is to book the action. No matter the game, let the players pick their own losers.

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                    Posted: March 4, 2007, 9:16 pm - IP Logged

                    "The odds of winning if one buys two tickets are cut in half. Whether those two tickets are purchased for the same or different drawings makes no difference, the odds are cut in half. Just as the odds are the odds, the mathematics are the mathematics. As was pointed out, 2::10,000,000 is the same as 1::5,000,000. That's math."  Johnph77

                     

                    Well, I don't want to keep getting into long discussions about this, but I'll try one more time. Thanks, Coin Toss. I'm glad someone here is paying attention.  I am not a stubborn person (quite the opposite) but I am a logical one. In fact, I'm not that great at math, but I am using common sense. Sure, if you buy one ticket and your neighbor buys 2 tickets or even 100 tickets, he definitely has more opportunities to win a jackpot. Do you know how many people spend $100 and don't get anything, not even 3 numbers?

                    Let's use a game where the odds are 1 in 140 million.  If there are 140 million combinations, how can buying just one more ticket wipe out the other 139,999,999 combinations?  To say that buying a second ticket cuts the odds from 1:140M to 1:70M doesn't make any sense to me at all. Mathematics is logical.  It is a science.  Buying one more ticket DOES NOT cut the odds in half, and this isn't just a matter of semantics - and if you think "that's math" it's fine with me.  I just hope you don't teach statistics or your students are all in big trouble.  Okay, I said I wasn't going to get into a lot of detail, but let me try one more time (as I have on so many other threads) to explain this step by step.

                    You have 140 million different combinations - buy 1 ticket

                    You have 139,999,999 different combinations left - buy another ticket

                    You have 139,999,998 different combinations left - buy a third ticket

                    You have 139,999,997 different combinations left - buy a fouth ticket

                    You have 139,999,996 different combinations left - buy a fifth ticket

                    You have 139,999,995 different combination lefts - buy a sixth ticket.

                    If you are crazy enough to spend $999K on one drawing, you will still have over 139 million combinations that might come up that you didn't pick.

                    So now maybe you can tell me how buying a second ticket cuts the odds in half and makes it 1 in 70M.  What happened to the rest of the combinations?  When the odds are 1 in 70M it means there are 70 million combinations.  But I just showed you above that you have over 139,999,998 combinations left after buying 2 tickets. What happened to the other 69,999,998 ? 

                    "John has it exactly right, assuming one ticket for each drawing.  The fact that a bunch of posters here don't understand the math doesn't change the facts. Having two tickets makes you twice as likely to win,"

                    KY Floyd, you can tell me that I don't understand a math equation and I might agree with you. But using convoluted logic to prove an invalid point won't change the fact that you are WRONG when you keep insisting that having 2 chances to win cuts the odds in half.  Using the example of 2/4 is silly.  Why not say the odds are 1 out of 1?  Let's keep it simple and make it 100.  A very easy game anyone can win, not MM or PB or even pick-3.  Buying 1 ticket gives you a 1 in 100 shot.  2 gives you a 2 in 100 shot, not 1 in 50.  Why? Because there are still 98 combinations you haven't bet on!   However, if you spend $50, you are cutting the odds in half.  So the way to cut the odds in half in a game where the odds are 1 in 140 million is to spend $70 million.

                    I've seen lotto websites (with an "s") say that if you buy 2 tickets the odds are reduced in half..Can't find the lotto websites right now but i've seen them...

                     

                     

                    "MOre important than winning the state's lotteries is the movie "Red Planet"...."

                      Coin Toss's avatar - shape barbed.jpg
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                      Posted: March 4, 2007, 11:02 pm - IP Logged

                      Once upon a time there was a lottery player named Henry Halves the Odds. We'll just call him Henry.

                      The Mega Millions jackpot was up so Henry went to play a ticket. He deicded on a quick pick this time and heade for a lotto outlet.

                      <insert Twilight Zone music here>.

                      This was a very unique lottery outlet, and behind the counter where the clerk ran your tickets was a board with 175,711,536 lights on it.

                      Henry asked the clerk what was with all the lights, and the clerk explained that there was a light for every possible combination given grids of 56 abd 46 on a 5 + 1 lottry. 

                      (This was a very special lottery outlet).

                      Henry handed the clerk a dollar and asked for a Mega Millions quixk pick. AQs the clerk ran the ticket one light went out.  Henry was kind of mesmerised seeing that one light go out, and thought to himself, "Wait a minute, I remember reading about playing a second ticket cutting the odds in half, and I'm going to make a whole bunch of light go out." 

                      He gave the clerk another dollar and asked for another quick pick. As the clerk ran the ticket, Henry was surpirsed when only one more light went out.

                      The clerk noticed Henry's surprised and asked him if he thought something else was going to happen. Henry said as a matter of fact, he did, he was sure that the second dollar was going to turn off half of the remaining lights, not just one of them. 

                      The clerk said, "Well if you remember that "magic bullet" theory in the movie JFK, a lot of lottery players come in here with what they think is a "magic dollar" that's going to put that "magic bullet" to shame, but it just doesn't happen. 

                      The clerk continued, "A few years ago lottery sales showed a decline, so the commission had agents go everywhere and start a rumor about one more dollar cutting the odds in half. Bars, lotto outlets, chat rooms, all those places."

                      Henry looke at his numbers and walked out of the story thinking to himself, "Son of s gun, only one more light went out." 

                      Those who run the lotteries love it when players look for consistency in something that's designed not to have any.

                      Lep

                      There is one and only one 'proven' system, and that is to book the action. No matter the game, let the players pick their own losers.

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                        Posted: March 4, 2007, 11:06 pm - IP Logged

                        Amusing story, Coin Toss.

                        Too bad it only happens like that in the land of make-believe.  Let me guess, he "walked right out of the story" and into a college math department where the professors explained to him that odds equals total combos divided by distinct tickets purchased, no more, no less.

                        Where is this thread headed anyway?  Yeesh.  Smile

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                          Posted: March 5, 2007, 12:12 am - IP Logged

                          Oh, the same place a lot of these go I guess. A few of us try to convince others that each line of numbers is but one combination up against over 176,000,000 possible combinations and that's all there is to it.

                          But they insist one  more combination they play is going to reduce those combinations by 85,000,000 all at once, not just by one more.

                          Then the lottery commission lurkers and "guests" that monitor this board poke thier co-workers and go, "Told ya. Poor bastards, poor dumb bastards." Then in a while the matrix expands again, but hey, that's ok because that "magic dollar" will cut those odds by half, too.

                          And people will continue to tell stories about the fabulous time they had at the 1994 World Series.  

                          Yeesh indeed.  

                          Those who run the lotteries love it when players look for consistency in something that's designed not to have any.

                          Lep

                          There is one and only one 'proven' system, and that is to book the action. No matter the game, let the players pick their own losers.

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                            Posted: March 5, 2007, 1:21 am - IP Logged

                            Not really, but I do agree we'll never agree this way.  Saying 2 tickets changes the odds of a 1 in 140 million odd game to 1 in 70 million is assuming that each ticket is only gambling on 1/2 of the combinations.  But when you have 2 tickets that are betting on all 140 million combinations, the odds are NOT cut in half.  Sure, I agree if you had 2 separate games where there were 70 million possibilities (and this also applies to games with lesser odds) then buying a ticket for each game would prove KY Floyd and John correct.  But that's not what is happening.  A person is buying 2 tickets for the same 140 million choices.  So buying 2 tickets just leaves 139,999,998 combinations left.  If the odds were cut in half as you say, then each ticket purchased would represent an equal number of combinations.  A simple way to look at your theory or example is to use a lottery pool.  If 2 tickets cut the odds in half, why wouldn't a pool where members buy 100 tickets (and there are many that buy 1,000) win all the time? The reason is that you are still betting on the original 140 million combinations. The way you state it, you are betting 1 ticket on 1/2 the combinations and the second on the other 1/2 and so on.  Hope I am being clear, but maybe we are on such different planes here that we'll never see it the same way.

                            Anyway, after reading this article on possibilities of ways to die, I think instead of buying lottery tickets, we should be investing in safety devices!  http://www.nsc.org/lrs/statinfo/odds.htm

                            Smiley 

                            I'll get to some of your other stuff later, but I think you might have given yourself a really good clue here.

                            "Saying 2 tickets changes the odds of a 1 in 140 million odd game to 1 in 70 million is assuming that each ticket is only gambling on 1/2 of the combinations."

                            Let's look at what you just said and apply it to pick 4. There are 10,000 possible outcomes, so the game odds are 1 in 10,000. Half of the 10,000 possible outcomes are odd and half are even. If you buy one ticket with an odd number and one ticket with an even number each ticket is gambling on only half of the possible combinations. If the winning number is odd there is a 1 in 5000 chance that  it will be the odd number you played. If the winning number is even there is a 1 in 5000 chance that  it will be the even number you played. That means that one of your two tickets has to have a 1 in 5000 chance of winning,and that means that between them the two tickets give you a 1 in 5000 chance of winning. Does that make sense?

                            "If 2 tickets cut the odds in half, why wouldn't a pool where members buy 100 tickets (and there are many that buy 1,000) win all the time?"

                            Because being 100 times more likley to win is basically meaningless when the game odds start at 100 million to 1 against winning. If the odds are 100 million to 1 against winning and  you buy 100 tickets the odds are still 1 million to 1 against you. Buying 100 tickets for every drawing still means you would only expect to win once every 9,615 years, assuming there are two draws a week.

                              justxploring's avatar - villiarna
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                              Posted: March 5, 2007, 1:42 am - IP Logged

                              If you buy one ticket with an odd number and one ticket with an even number each ticket is gambling on only half of the possible combinations.

                              Why?  If you buy 2 tickets, no matter what numbers you select to play, they are each betting on all 10,000 of the combinations.