Mission146
Mission146 
Joined: May 15, 2012
  • Threads: 132
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Thanks for this post from:
seven
September 15th, 2021 at 7:27:41 AM permalink
Quote: seven



thank you very much for the formula as it looks like it answers my question but please be so kind if you can give it to me ELI5
for example I know that a single zero roulette has a - 0.027 EV for the player means 2.7% house advantage
what is the EV for the Player in % of your result 1.14285714286 (This assumes only one winner of $450)
and 3.27652623351

cheers

  • link to original post



    You're welcome!

    Okay, you want to determine his EV whereas we have calculated his expected return. We know that he is betting a grand total of $1 paid for his ten tickets, so this will be a simple matter of dividing his expectation by the amount he is betting.

    1.14285714286/1 = 1.14285714286 (or 114.2857%, rounded)

    3.27652623351/1 = 3.27652623351 (or 327.6526%, rounded)

    The fact that he only paid a dollar made this slightly easier. If he had paid a total of $2 for the tickets, here is what it would look like with one winner of $450:

    (448 * (10/2100)) - (2 * (2090/2100) = 0.14285714285

    Okay, so that solves for his expected return if he had paid $2 for the tickets, so with that:

    0.14285714285/2 = 0.07142857142. (This means he has a 7.142857%, rounded, advantage)

    Naturally, he would be at a disadvantage had he paid $10 for ten tickets, so let's see what that would look like:

    (440 * (10/2100)) - (10 * (2090/2100) = -7.85714285714

    -7.85714285714/10 = -0.78571428571 (This represents a 78.57143%, rounded, disadvantage, Yikes!)
    https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
    seven
    seven
    Joined: Oct 1, 2013
    • Threads: 18
    • Posts: 167
    Thanks for this post from:
    Mission146
    September 15th, 2021 at 7:38:01 AM permalink
    Quote: Mission146

    Quote: seven



    thank you very much for the formula as it looks like it answers my question but please be so kind if you can give it to me ELI5
    for example I know that a single zero roulette has a - 0.027 EV for the player means 2.7% house advantage
    what is the EV for the Player in % of your result 1.14285714286 (This assumes only one winner of $450)
    and 3.27652623351

    cheers

  • link to original post



    You're welcome!

    Okay, you want to determine his EV whereas we have calculated his expected return. We know that he is betting a grand total of $1 paid for his ten tickets, so this will be a simple matter of dividing his expectation by the amount he is betting.

    1.14285714286/1 = 1.14285714286 (or 114.2857%, rounded)

    3.27652623351/1 = 3.27652623351 (or 327.6526%, rounded)

    The fact that he only paid a dollar made this slightly easier. If he had paid a total of $2 for the tickets, here is what it would look like with one winner of $450:

    (448 * (10/2100)) - (2 * (2090/2100) = 0.14285714285

    Okay, so that solves for his expected return if he had paid $2 for the tickets, so with that:

    0.14285714285/2 = 0.07142857142. (This means he has a 7.142857%, rounded, advantage)

    Naturally, he would be at a disadvantage had he paid $10 for ten tickets, so let's see what that would look like:

    (440 * (10/2100)) - (10 * (2090/2100) = -7.85714285714

    -7.85714285714/10 = -0.78571428571 (This represents a 78.57143%, rounded, disadvantage, Yikes!)
  • link to original post



    great! thanks again. that is exactly what I wanted to understand as it is an immense high +EV for the player. especially the 2 prizes version confused me and now I understand why as the +EV (player) is so high and I could not believe it.
    now I can use your formula to get the player's EV if he has 9-8-7 .... etc tickets
    stay safe
    Mission146
    Mission146 
    Joined: May 15, 2012
    • Threads: 132
    • Posts: 14617
    September 15th, 2021 at 7:40:34 AM permalink
    Thank you very much! You're welcome! Not only using the formula for that, but you'll also know how to do it in the future for different numbers of total tickets, individual tickets and/or cash spent.
    https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
    seven
    seven
    Joined: Oct 1, 2013
    • Threads: 18
    • Posts: 167
    Thanks for this post from:
    Mission146
    September 15th, 2021 at 8:00:23 AM permalink
    Quote: Mission146

    Thank you very much! You're welcome! Not only using the formula for that, but you'll also know how to do it in the future for different numbers of total tickets, individual tickets and/or cash spent.

  • link to original post



    yes I did now the math for one prize and 9 tickets down to one ticket. this was very helpful, thanks again
    but I didn't see or oversaw the formula for the 2 prizes
    I saw this one you gave: ((0.00476190476+0.00474148687)*449) - (1 * 0.99049660836) = 3.27652623351 (This is ten tickets with two winners of $450, but the same person cannot win twice)
    how can I do the math for 9-8-7 etc ?

    cheers
    Mission146
    Mission146 
    Joined: May 15, 2012
    • Threads: 132
    • Posts: 14617
    Thanks for this post from:
    seven
    September 15th, 2021 at 8:24:00 AM permalink
    Quote: seven

    Quote: Mission146

    Thank you very much! You're welcome! Not only using the formula for that, but you'll also know how to do it in the future for different numbers of total tickets, individual tickets and/or cash spent.

  • link to original post



    yes I did now the math for one prize and 9 tickets down to one ticket. this was very helpful, thanks again
    but I didn't see or oversaw the formula for the 2 prizes
    I saw this one you gave: ((0.00476190476+0.00474148687)*449) - (1 * 0.99049660836) = 3.27652623351 (This is ten tickets with two winners of $450, but the same person cannot win twice)
    how can I do the math for 9-8-7 etc ?

    cheers
  • link to original post



    For that one, you're going to have to go back to an earlier post and change the probabilities, because there are now fewer tickets.

    You may remember this:

    Quote:

    Okay, there are three possible combinations of events that can happen in this one. What we're going to do here is express them in the simplest terms:

    1.) The first ticket drawn results in the guy winning:

    10/2100 = 0.00476190476

    2.) He does not win on the first ticket, but then he does win on the second ticket drawn:

    (2090/2100) * (10/2099) = 0.00474148687

    3.) He does not win on either ticket drawn:

    (2090/2100) * (2089/2099) = 0.99049660836

    Okay, so we know that he either wins $450 (which is really $440 profits because he paid for the tickets) or that he loses $10. With that, we have:

    ((0.00476190476+0.00474148687)*440) - (10 * 0.99049660836) = -5.7234737664



    Okay, so now you want him to have nine tickets total, if I am understanding you correctly, so you have to change the probabilities:

    1.) The first ticket drawn results in the guy winning:

    9/2100 = 0.00428571428

    2.) He does not win on the first ticket, but then he does win on the second ticket drawn:

    (2091/2100) * (9/2099) = 0.00426937997

    3.) He does not win on either ticket drawn:

    (2091/2100) * (2090/2099) = 0.99144490573

    Okay, so we will say that he spends one dollar on these nine tickets and will either win $449 (profits) or lose the $1:

    ((0.00428571428+0.00426937997) * 449) - (1 * 0.99144490573) = 2.84979241252

    And, he's only spending a dollar, so for his Expected Return Percentage, you just move the decimal place two to the right and get 284.97924%, rounded.

    CHANGE NUMBER OF TICKETS---Steps 1 Through 3 (You can also change the total number of tickets in the pool)

    CHANGE EXPECTATION DUE TO CASH SPENT---Change the dollar amounts in the last step to reflect potential profit and cash spent.
    https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
    seven
    seven
    Joined: Oct 1, 2013
    • Threads: 18
    • Posts: 167
    September 15th, 2021 at 8:42:55 AM permalink
    Quote: Mission146

    Quote: seven

    Quote: Mission146

    Thank you very much! You're welcome! Not only using the formula for that, but you'll also know how to do it in the future for different numbers of total tickets, individual tickets and/or cash spent.

  • link to original post



    yes I did now the math for one prize and 9 tickets down to one ticket. this was very helpful, thanks again
    but I didn't see or oversaw the formula for the 2 prizes
    I saw this one you gave: ((0.00476190476+0.00474148687)*449) - (1 * 0.99049660836) = 3.27652623351 (This is ten tickets with two winners of $450, but the same person cannot win twice)
    how can I do the math for 9-8-7 etc ?

    cheers
  • link to original post



    For that one, you're going to have to go back to an earlier post and change the probabilities, because there are now fewer tickets.

    You may remember this:



    Okay, so now you want him to have nine tickets total, if I am understanding you correctly, so you have to change the probabilities:

    1.) The first ticket drawn results in the guy winning:

    9/2100 = 0.00428571428

    2.) He does not win on the first ticket, but then he does win on the second ticket drawn:

    (2091/2100) * (9/2099) = 0.00426937997

    3.) He does not win on either ticket drawn:

    (2091/2100) * (2090/2099) = 0.99144490573

    Okay, so we will say that he spends one dollar on these nine tickets and will either win $449 (profits) or lose the $1:

    ((0.00428571428+0.00426937997) * 449) - (1 * 0.99144490573) = 2.84979241252

    And, he's only spending a dollar, so for his Expected Return Percentage, you just move the decimal place two to the right and get 284.97924%, rounded.

    CHANGE NUMBER OF TICKETS---Steps 1 Through 3 (You can also change the total number of tickets in the pool)

    CHANGE EXPECTATION DUE TO CASH SPENT---Change the dollar amounts in the last step to reflect potential profit and cash spent.
  • link to original post



    thank you so much for taking the time to explain it again and ELI5, very very much appreciated!
    Stay safe and God Bless You and Your Family
    Mission146
    Mission146 
    Joined: May 15, 2012
    • Threads: 132
    • Posts: 14617
    September 15th, 2021 at 8:52:23 AM permalink
    You're very welcome! Thanks for the questions and have a great day!
    https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
    seven
    seven
    Joined: Oct 1, 2013
    • Threads: 18
    • Posts: 167
    September 15th, 2021 at 12:25:32 PM permalink
    Quote: Mission146

    You're very welcome! Thanks for the questions and have a great day!

  • link to original post



    I am really sorry to bother you again. I did now the math but I am not sure if I am correct or I messed up! would you be so kind whenever you have the time to go over my results? would be very much appreciated.

    1 prize EV
    10 tickets EV is + 114.28 %
    9 tickets EV is + 92.9 %
    8 tickets EV is + 72 %
    7 tickets EV is + 50 %
    6 tickets EV is + 29 %
    5 tickets EV is + 7.4 %
    4 tickets EV is - 14 %
    3 tickets EV is - 35.4 %
    2 tickets EV is - 56.8 %
    1 ticket EV is - 78.1 %

    2 prizes EV
    9 tickets EV is + 284.98 %
    8 tickets EV is + 242.29 %
    7 tickets EV is + 199.57 %
    6 tickets EV is + 156.84 %
    5 tickets EV is + 114.08 %
    4 tickets EV is + 71.30 %
    3 tickets EV is + 28.51 %
    2 tickets EV is - 14.30 %
    1 ticket EV is - 57.14 %
    seven
    seven
    Joined: Oct 1, 2013
    • Threads: 18
    • Posts: 167
    September 17th, 2021 at 7:23:49 AM permalink
    another question I am asking myself and @all if 2 Prizes of $450 or 1 Prize of $900 is more attractive for the participants?

    cheers

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