seven
Joined: Oct 1, 2013
• Posts: 173
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September 14th, 2021 at 8:30:56 AM permalink
hi @all

let's say a lottery participant has 10 tickets which costs him all in all \$1 in a lottery game with 2100 tickets. There will be a draw with 2 winners who get \$450 each.

What is the player's EV?

I am confused about the 2 winners of the draw

cheers
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 5417
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September 14th, 2021 at 8:41:28 AM permalink
There are C(2100, 2) = 2,203,950 pairs of winning tickets.
There are three possible results as far as the player is concerned:

1. There are 45 pairs where the player has both tickets; the ER (expected return) of this is 45 / 2,203,950 x 900

2. There are 10 x 2090 = 20,900 pairs where the player has one ticket; the ER is 20,900 / 2,203,950 x 450.

3. There are C(2090, 2) pairs where the player wins nothing.

The total ER is 9,445,000 / 2,203,950 = 30/7.
Since the player paid 10 for the tickets, the EV is (30/7 - 10) = -40/7.
seven
Joined: Oct 1, 2013
• Posts: 173
September 14th, 2021 at 10:07:55 AM permalink
Quote: ThatDonGuy

There are C(2100, 2) = 2,203,950 pairs of winning tickets.
There are three possible results as far as the player is concerned:

1. There are 45 pairs where the player has both tickets; the ER (expected return) of this is 45 / 2,203,950 x 900

2. There are 10 x 2090 = 20,900 pairs where the player has one ticket; the ER is 20,900 / 2,203,950 x 450.

3. There are C(2090, 2) pairs where the player wins nothing.

The total ER is 9,445,000 / 2,203,950 = 30/7.
Since the player paid 10 for the tickets, the EV is (30/7 - 10) = -40/7.

thank you very much for the answer but I need to apologize that I did not explain correctly/understandable. I am really sorry

the player who has 10 tickets paid \$1 for all the 10 tickets ( he did not pay \$10 for the 10 tickets)

the 2 winner prizes will go to 2 separate players means if one player wins he can not win the 2nd prize

I hope I could clear it up now

cheers

edit
maybe I should explain the 2100 tickets draw
there will be 2100 tickets in a hat and one ticket will be drawn for the 1st winner then there will be drawn another ticket for the 2nd winner. if the 1st winner will win again it will not count and another ticket will be drawn
Mission146
Joined: May 15, 2012
• Posts: 15308
September 14th, 2021 at 10:32:06 AM permalink
Quote: seven

thank you very much for the answer but I need to apologize that I did not explain correctly/understandable. I am really sorry

the player who has 10 tickets paid \$1 for all the 10 tickets ( he did not pay \$10 for the 10 tickets)

the 2 winner prizes will go to 2 separate players means if one player wins he can not win the 2nd prize

I hope I could clear it up now

cheers

edit
maybe I should explain the 2100 tickets draw
there will be 2100 tickets in a hat and one ticket will be drawn for the 1st winner then there will be drawn another ticket for the 2nd winner. if the 1st winner will win again it will not count and another ticket will be drawn

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

This is only slightly worse than what ThatDonGuy ended up with and the reason why is simply that the guy cannot win twice. It also assumes that the original \$10 for the tickets is sunk (pays on a For One basis) even if he wins.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
seven
Joined: Oct 1, 2013
• Posts: 173
September 14th, 2021 at 10:49:46 AM permalink
Quote: Mission146

Quote: seven

thank you very much for the answer but I need to apologize that I did not explain correctly/understandable. I am really sorry

the player who has 10 tickets paid \$1 for all the 10 tickets ( he did not pay \$10 for the 10 tickets)

the 2 winner prizes will go to 2 separate players means if one player wins he can not win the 2nd prize

I hope I could clear it up now

cheers

edit
maybe I should explain the 2100 tickets draw
there will be 2100 tickets in a hat and one ticket will be drawn for the 1st winner then there will be drawn another ticket for the 2nd winner. if the 1st winner will win again it will not count and another ticket will be drawn

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

This is only slightly worse than what ThatDonGuy ended up with and the reason why is simply that the guy cannot win twice. It also assumes that the original \$10 for the tickets is sunk (pays on a For One basis) even if he wins.

I don't understand why 3 possible combinations

the player with 10 tickets in case one of his tickets is drawn out of the hat will win \$450 minus \$1 equals \$449 profit. the winner ticket is out and does not go back into the hat.

in case the next ticket which is drawn is also from the player who owns 10 tickets the ticket is out of the hat and another ticket is drawn until a 2nd winner is drawn

what is the EV of the player with 10 tickets?
Mission146
Joined: May 15, 2012
• Posts: 15308
September 14th, 2021 at 11:19:48 AM permalink
Quote: seven

I don't understand why 3 possible combinations

the player with 10 tickets in case one of his tickets is drawn out of the hat will win \$450 minus \$1 equals \$449 profit. the winner ticket is out and does not go back into the hat.

in case the next ticket which is drawn is also from the player who owns 10 tickets the ticket is out of the hat and another ticket is drawn until a 2nd winner is drawn

what is the EV of the player with 10 tickets?

Your original post stipulated that he has ten tickets. Is he going to get a refund on the nine that don't win? If you want to know his EV, then it includes the fact that he has purchased ten tickets.

Three combinations because:

His ticket could be the first drawn: 10/2100 is the probability of that event. 0.00476190476

His ticket could be the second drawn, which means some other ticket was drawn first: (2090/2100 * 10/2099) = 0.00474148687 (As you can see, this is slightly less likely than one of his tickets being the first drawn, mainly just because it includes another event happening)

Both tickets drawn are none of his ten.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
Mission146
Joined: May 15, 2012
• Posts: 15308
September 14th, 2021 at 11:24:08 AM permalink
Or, are you saying that the tickets cost a TOTAL of \$1?

If that's the case, just replace "440" and "10":

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

With "449" and "1", respectively.
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
seven
Joined: Oct 1, 2013
• Posts: 173
September 14th, 2021 at 11:27:20 AM permalink
Quote: Mission146

Quote: seven

I don't understand why 3 possible combinations

the player with 10 tickets in case one of his tickets is drawn out of the hat will win \$450 minus \$1 equals \$449 profit. the winner ticket is out and does not go back into the hat.

in case the next ticket which is drawn is also from the player who owns 10 tickets the ticket is out of the hat and another ticket is drawn until a 2nd winner is drawn

what is the EV of the player with 10 tickets?

Your original post stipulated that he has ten tickets. Is he going to get a refund on the nine that don't win? If you want to know his EV, then it includes the fact that he has purchased ten tickets.

sorry for the confusion. he purchased 1 ticket for \$1 and got another 9 for free so he has 10 tickets for \$1 and he did not pay \$10 for ten tickets. he does not get any refund.
as my confusion was because of the 2 winner option maybe we try the simple option with one prize winner of \$450. in the hat are 2100 tickets and there will be drawn 1 ticket and the winner gets \$450. what is the EV for a player with 10 tickets he paid \$1 for all ten tickets ( he did not pay \$10 for the ten tickets)?
Mission146
Joined: May 15, 2012
• Posts: 15308
Thanks for this post from:
September 14th, 2021 at 11:47:46 AM permalink
Quote: seven

sorry for the confusion. he purchased 1 ticket for \$1 and got another 9 for free so he has 10 tickets for \$1 and he did not pay \$10 for ten tickets. he does not get any refund.
as my confusion was because of the 2 winner option maybe we try the simple option with one prize winner of \$450. in the hat are 2100 tickets and there will be drawn 1 ticket and the winner gets \$450. what is the EV for a player with 10 tickets he paid \$1 for all ten tickets ( he did not pay \$10 for the ten tickets)?

(449 * (10/2100)) - (1 * (2090/2100) = 1.14285714286 (This assumes only one winner of \$450)

((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)
https://wizardofvegas.com/forum/off-topic/gripes/11182-pet-peeves/120/#post815219
seven
Joined: Oct 1, 2013
• Posts: 173
September 14th, 2021 at 11:10:01 PM permalink
Quote: Mission146

Quote: seven

sorry for the confusion. he purchased 1 ticket for \$1 and got another 9 for free so he has 10 tickets for \$1 and he did not pay \$10 for ten tickets. he does not get any refund.
as my confusion was because of the 2 winner option maybe we try the simple option with one prize winner of \$450. in the hat are 2100 tickets and there will be drawn 1 ticket and the winner gets \$450. what is the EV for a player with 10 tickets he paid \$1 for all ten tickets ( he did not pay \$10 for the ten tickets)?

(449 * (10/2100)) - (1 * (2090/2100) = 1.14285714286 (This assumes only one winner of \$450)

((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)

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