Welcome Guest
Log In | Register )
You last visited January 18, 2017, 11:21 pm
All times shown are
Eastern Time (GMT-5:00)

A comment on the new Powerball Expectation Values.

Topic closed. 11 replies. Last post 8 years ago by ThatScaryChick.

Page 1 of 1
PrintE-mailLink
Avatar
New Jersey
United States
Member #21206
September 4, 2005
949 Posts
Offline
Posted: January 4, 2009, 3:34 pm - IP Logged

In the old 5/55 form of Powerball, the expectation value for the lower prizes - the sum of the payouts for each prize divided by its odds was 0.20 total.   (This ignores the Powerplay, which I never play).

The new expectation value for the lower prizes has FALLEN to 0.17, meaning that the powerball - even though the probability of winning ANY prize is slightly higher - is actually, predictably, a worse bet than before.

The expectation value for the jackpot varies with the jackpot, and is a function of sales AND odds as well, since there will be a distribution for the probability of number of winners depending on the number of tickets sold.

Single winners are now more probable, but the probability of winning is much lower.     (Sales are down on average for all the lotteries I follow overall.)

Since the economy is collapsing and people are temporarily seeking bonds as a refuge (not that this refuge will hold) the ratio of the cash value to the annuity value is at historical highs.

The current "105 million" dollar jackpot currently produces an overall expectation value of 0.50, meaning that the ration of reward to risk is about 0.5.    This compares to casinos at 0.9, casinos probably being more reliable than the stock market.

Occassionally, with very high jackpots, the expectation value would actually reach a value close to, or even exceeding 1.0.   

The old Powerball twice reached 19 draws, averaging 163,000,000 in sales.   This number of sales would obviously not even cover the field under the new, regrettable, conditions.    The rollover probability in this case would be around 43% with the new odds.

In order to have an overall expectation value of 1.00, a jackpot with this number sales would have to be at least 320,000,000 annuity (at the current cash ratio.)   

My expectation value figures do NOT include taxes.

Since I play according to expectation values, I will be playing less powerball than before.

    Guru101's avatar - rw6jhh
    Indiana
    United States
    Member #48725
    January 7, 2007
    1958 Posts
    Offline
    Posted: January 4, 2009, 6:46 pm - IP Logged

    I'll probably play the same as I usually do. Even though there's about 50 million more combinations, we're talking about a game that makes state lotto games look puny. In my opinion, both before and now, the odds are so high in this game that it's not really about what your odds are, it's about whether or not you have a ticket, even it's just $1.

    Gonna win.Big Smile

      BaristaExpress's avatar - BaristaExpressMX zpsfb0d8b5d.png
      Magnolia, Delaware
      United States
      Member #18795
      July 20, 2005
      789 Posts
      Offline
      Posted: January 4, 2009, 9:30 pm - IP Logged

      I'll probably play the same as I usually do. Even though there's about 50 million more combinations, we're talking about a game that makes state lotto games look puny. In my opinion, both before and now, the odds are so high in this game that it's not really about what your odds are, it's about whether or not you have a ticket, even it's just $1.

      I Agree!

      Keep dreaming the impossible dream, it just may come true! Thumbs Up


        Canada
        Member #68663
        December 27, 2008
        260 Posts
        Offline
        Posted: January 5, 2009, 12:11 am - IP Logged

        Prob988,

        Good analysis. I agree with most of it except I take real exception to how you calculate the expected value. It is imperative that you include the taxes. It is not correct to ignore when calculating the value of a wager. Especially since they reduce the amount won by such a large amount. It is misleading and some people will decide to play based on your analysis when you report an expected value of close to 1.00. I realize that the amount of taxes a person will pay will vary but at least include a minimum amount of at least 25%.

          ThatScaryChick's avatar - x1MqPuM
          Idaho
          United States
          Member #56506
          November 21, 2007
          6537 Posts
          Offline
          Posted: January 5, 2009, 12:13 am - IP Logged

          I'll probably play the same as I usually do. Even though there's about 50 million more combinations, we're talking about a game that makes state lotto games look puny. In my opinion, both before and now, the odds are so high in this game that it's not really about what your odds are, it's about whether or not you have a ticket, even it's just $1.

          Unfortunately, I won't be. I may put in a dollar or two every now and then, but I now will be focusing on games with better odds.

          "No one remembers the person who almost climbed the mountain, only the person who eventually gets to the top."

            adulane62's avatar - file php?avatar=16228.gif
            From Denver, Rocky Mountain Empire,
            United States
            Member #49750
            February 13, 2007
            448 Posts
            Offline
            Posted: January 5, 2009, 11:30 pm - IP Logged

            In the old 5/55 form of Powerball, the expectation value for the lower prizes - the sum of the payouts for each prize divided by its odds was 0.20 total.   (This ignores the Powerplay, which I never play).

            The new expectation value for the lower prizes has FALLEN to 0.17, meaning that the powerball - even though the probability of winning ANY prize is slightly higher - is actually, predictably, a worse bet than before.

            The expectation value for the jackpot varies with the jackpot, and is a function of sales AND odds as well, since there will be a distribution for the probability of number of winners depending on the number of tickets sold.

            Single winners are now more probable, but the probability of winning is much lower.     (Sales are down on average for all the lotteries I follow overall.)

            Since the economy is collapsing and people are temporarily seeking bonds as a refuge (not that this refuge will hold) the ratio of the cash value to the annuity value is at historical highs.

            The current "105 million" dollar jackpot currently produces an overall expectation value of 0.50, meaning that the ration of reward to risk is about 0.5.    This compares to casinos at 0.9, casinos probably being more reliable than the stock market.

            Occassionally, with very high jackpots, the expectation value would actually reach a value close to, or even exceeding 1.0.   

            The old Powerball twice reached 19 draws, averaging 163,000,000 in sales.   This number of sales would obviously not even cover the field under the new, regrettable, conditions.    The rollover probability in this case would be around 43% with the new odds.

            In order to have an overall expectation value of 1.00, a jackpot with this number sales would have to be at least 320,000,000 annuity (at the current cash ratio.)   

            My expectation value figures do NOT include taxes.

            Since I play according to expectation values, I will be playing less powerball than before.

            I will play powerball the same way. I never expect to win powerball, but if I do more power to me! All lotteries are a game of chance, regardless of the odds. Play responsibly and have fun!    Guitar

              Avatar
              New Jersey
              United States
              Member #21206
              September 4, 2005
              949 Posts
              Offline
              Posted: January 7, 2009, 1:32 am - IP Logged

              Prob988,

              Good analysis. I agree with most of it except I take real exception to how you calculate the expected value. It is imperative that you include the taxes. It is not correct to ignore when calculating the value of a wager. Especially since they reduce the amount won by such a large amount. It is misleading and some people will decide to play based on your analysis when you report an expected value of close to 1.00. I realize that the amount of taxes a person will pay will vary but at least include a minimum amount of at least 25%.

              Why?

              If someone says "I make $120,000/year" we generally assume he or she doesn't mean "after taxes."

              People who win at Casinos - who are often required to pay taxes - similarly don't announce it as such.

              Why should winning the lottery be different than say, getting to steal huge amounts of money as a CEO of say, Wachovia Bank?

                justxploring's avatar - villiarna
                Wandering Aimlessly
                United States
                Member #25360
                November 5, 2005
                4461 Posts
                Offline
                Posted: January 7, 2009, 1:59 am - IP Logged

                Why?

                If someone says "I make $120,000/year" we generally assume he or she doesn't mean "after taxes."

                People who win at Casinos - who are often required to pay taxes - similarly don't announce it as such.

                Why should winning the lottery be different than say, getting to steal huge amounts of money as a CEO of say, Wachovia Bank?

                I Agree!

                I am trying not to purchase any PB tickets, since I am already spending too much, but it's tempting.

                My experience talking to customers at lottery retailers tells me most people don't really think about the odds.  Over $1.5 million PB tickets were sold in FL in the first 2 days.  One woman tonight bought a PB ticket and asked "is it just like Lotto?"  I mentioned that the jackpot is currently much higher, but the odds of winning it are 1:195 million.  She answered "Well, then it's just like Lotto." (FL Lotto's odds are 1:23 million.) So to many people, especially those who buy only QPs, it doesn't seem to matter.

                  Avatar
                  NY
                  United States
                  Member #23835
                  October 16, 2005
                  3502 Posts
                  Offline
                  Posted: January 7, 2009, 3:56 am - IP Logged

                  Why?

                  If someone says "I make $120,000/year" we generally assume he or she doesn't mean "after taxes."

                  People who win at Casinos - who are often required to pay taxes - similarly don't announce it as such.

                  Why should winning the lottery be different than say, getting to steal huge amounts of money as a CEO of say, Wachovia Bank?

                  For the same reason that you wouldn't use the annuity value. The only point of calculating an expectation value is to make the risk to reward an objective  quantity. The expectation value is only as realistic as the numbers you use to calculate it, so it has to be based on what you'll actually get and not some imaginary number. For odds of 1 in 195 million the expectation value isn't 1 unless the net is $195 million. Unless perhaps you actually want to share the prize with the government.

                  Of course that means that your expectation value and mine may be somewhat different, because our tax situation wil be different, but that difference is far smaller than the impact of taxes in general. Similarly, there's a bit of a risk that the prize will be split, and the realized value would be 1/2 or 1/3 of the expectation value, but that's a relatively small risk.


                    United States
                    Member #9579
                    December 12, 2004
                    2121 Posts
                    Offline
                    Posted: January 7, 2009, 9:19 am - IP Logged

                    it's just an honest way for the states to apply a huge education tax for students,so after they graduate,can get laid off!

                      justxploring's avatar - villiarna
                      Wandering Aimlessly
                      United States
                      Member #25360
                      November 5, 2005
                      4461 Posts
                      Offline
                      Posted: January 7, 2009, 5:30 pm - IP Logged

                      I am so proud of myself!  Big Grin

                      I bought 4 Lotto tickets and 2 Fantasy5 tickets tonight.  No PB. Yay!  I was able to walk away.

                      Everyone is so excited about PB in Florida, so it was very tempting, but I can't spend any more money without the lottery becoming a burden, if not an obsession. 

                      Still, I wish everyone good luck tonight.  Maybe someone here will win the $105 million.

                        ThatScaryChick's avatar - x1MqPuM
                        Idaho
                        United States
                        Member #56506
                        November 21, 2007
                        6537 Posts
                        Offline
                        Posted: January 7, 2009, 6:48 pm - IP Logged

                        I am so proud of myself!  Big Grin

                        I bought 4 Lotto tickets and 2 Fantasy5 tickets tonight.  No PB. Yay!  I was able to walk away.

                        Everyone is so excited about PB in Florida, so it was very tempting, but I can't spend any more money without the lottery becoming a burden, if not an obsession. 

                        Still, I wish everyone good luck tonight.  Maybe someone here will win the $105 million.

                        I wasn't planning on getting any, but when I bought my Hot Lotto tickets, I decided to get one quick pick.

                        "No one remembers the person who almost climbed the mountain, only the person who eventually gets to the top."