Postby abloom » Thu Jul 09, 2020 5:52 am
mild wrote: ↑Thu Jul 09, 2020 5:00 am
trc wrote: ↑Thu Jul 09, 2020 3:29 am
It doesn't matter if you take them out or leave them in. The relative likelihood is all the same, as there is only x valid tickets in the bowl.
For example, if the team with the 10 tickets gets drawn the first draw - there are 9 non-valid tickets in the bowl.
So it's 55 tickets total in a 10 + 9 + 8 + 7... setup.
Does the league winner with 1 ticket have a better shot of drawing that ticket in a bowl of 54 tickets, or in a bowl of 45 tickets?
A draw for a non-valid ticket is a push, and triggers a re-draw - but it still puts the 1-in-54 ticket in a less probabilistic situation, and gives the other more probable tickets a 2nd chance at hitting their probabilities.
You're welcome

ps. don't gamble!
... wait are you saying that if there are 54 tickets (9 invalid triggering redraws, 44 tickets that would not win for the league winner, and 1 ticket that would be a win for the league winner) that it is different than 45 tickets (1 ticket that would be a win for the league winner)?
Because if so...
There is one way to win in the second option with a 1/45 chance (thats simple and can be agreed upon right?)
There are 10 ways of winning with the first option.
(1) 1/54
(2) 9/54 x 1/53
(3) 9/54 x 8/53 x 1/52
(4) 9/54 x 8/53 x 7/52 x 1/51
(5) 9/54 x 8/53 x 7/52 x 6/51 x 1/50
(6) 9/54 x 8/53 x 7/52 x 6/51 x 5/50 x 1/49
(7) 9/54 x 8/53 x 7/52 x 6/51 x 5/50 x 4/49 x 1/48
(8) 9/54 x 8/53 x 7/52 x 6/51 x 5/50 x 4/49 x 3/48 x 1/47
(9) 9/54 x 8/53 x 7/52 x 6/51 x 5/50 x 4/49 x 3/48 x 2/47 x 1/46
(10) 9/54 x 8/53 x 7/52 x 6/51 x 5/50 x 4/49 x 3/48 x 2/47 x 1/46 x 1/45
The sum of all these ways of winning = 1/45
So if you remove the invalid tickets you have a 1/45 chance, and if you don't remove it you have a 1/45 chance
I feel like I'm doing way to many math classes in this forum....
Last edited by
abloom on Thu Jul 09, 2020 8:39 am, edited 1 time in total.
Dynasty Team #1:
12 team, 1 ppr (1.5 te), 1Q,2R,2W,1T,2F,1D,1K
Q: Wentz,Tannehill,Hill
R: CMC,Taylor,Robinson,Fournette
W: Evans,Edelman,Cobb,Davis,Mooney,Lazard
T: Goedert(IR),Henry
D: NE,BAL
K: Bullock
2021 Picks: 1.02,2.05,4.02,5.02,6.02,7.02
---
Dynasty Team #2: 2020 Champion
12 team, 1ppr (1.5 te), 1Q,2R,2W,1T,1SF,1F,1D,1K
Q: Wilson, Murray, Cousins, Trubisky, Smith, Dalton
R: Cook, Dobbins, Swift, Monty, Mattison
W: Nuk, Godwin, Metcalf, K Allen, Sutton
T: Kelce
K: Tucker
D: PIT
2021 picks: 1.05,1.12,4.06,4.12,5.12,6.12,7.07
---
DLF advice forum league:
14 team, SF, 1PPR (2PPR for TE), 1Q,2R,3W,1T,1SF,2F
Q: Mahomes ,Tua, Mullens, Love, Flacco, Hoyer, Rypien, Bethard
R: Michel, Moss, Hyde, Bernard, Richard, Darrel Williams, Damien Williams, C Thompson
W: Juju, Cooper, Allen, Sanders, D Moore
T: Schultz, Doyle, Asiasi, Thomas
2021 Picks: 1.04,1.11,1.12,2.04,3.04,4.04,4.06,4.10