Say you have a standard deck and both jokers in it (54 cards obv) and you have them placed in different envelopes which their are no duplicates what would be the odds of needing to pull a certain card (say ace of hearts) and having pulled 46 total cards without it still remaining in an envelope? Is their any genius here that can figure it out or a program I can do that with?

Basically their is this raffle contest that has carried over for 46 weeks without the card being pulled at this local bar. It's a charity raffle but the jackpot is progressive carrying over each week and is now around $400k from $1 tickets along the way. The winner whose ticket gets pulled puts a number on it of which envelope they want from the ones remaining and that is the one pulled for the week. They get something for winning plus a potential bonus depending on what card is pulled but if they get the card needed to win they get the entire jackpot.

So, mathematically can anyone tell me the odds that the first 46 out of 54 cards pulled weren't that the ace of hearts?

8!/54!

that's a guess btw, i know that's probably way off.

Quick question: In week one, an envelope was pulled, card looked at(Tc), not a winner. Is that card then put back into the mix before week two? Or, is the Tc tossed aside, as well as other losing cards?

No cards are removed permanently and not recycled back in.

Oh and of course I know the odds now to hit next week but I'm wondering of course what they are that it wouldn't have been pulled in 46 straight cards.

the only thing i could think of was using a hypergeometric probability distribution.

i keep getting 14.8148148%

Setting N=54 n = 46 r = 0 Y = 1

which i mean i guess kind of makes sense, and i'm kind of an idiot because it just ends up being 8/54

Hmm.. I'll keep that idea in mind. I know it of course keeps reducing as it goes each week with one more card removed but I just figured maybe their was some odds calc thingy that could give me a better idea even it was based on a card deck it would likely be of just 52 cards and not 54.

i have no clue i poured through one of my old statistics book.

i went to psu and was 3 credits away from a minor in statistics, and i'm now realizing that transferring to another school was probably the best idea i've ever had.

I'd like to help and I'm sure others would too, but to be honest you've confused the shit out of me as to how this actually works.

I'll try and rephrase it differently.

1. You have a standard deck of cards plus the jokers so 54 cards.

2. You are trying to pull the ace of hearts from it which you pull 46 cards out one by one and still haven't pulled the ace of hearts.

3. We are not recycling cards back into the deck as once a card is pulled it stays out so it starts from a 1 in 54 chance of getting it then 1 in 53 , 1 in 52,etc... until it is pulled which means each time your odds keep improving.

4. What I'm wondering is approximately what the odds are that you would have pulled 46 of the 54 cards out one by one like this without pulling the ace of hearts?

I hope that makes a bit more sense as I'm not sure how else really to phrase it.

(53!/54!)/(7!/8!) roughly 15%

or 53*52*...8/ 54*53* ... 9

EDIT: and yes this = 8/54

Well two opinions of it so I will take 15% as being close enough unless someone else can prove otherwise which post here if you have another theory.

Thanks guys! I was thinking somewhere around a few percent less then that but can definitely see that being about right.

i think that analysis is kind one would make if there is concern that the lottery was not honest

really with 8 cards left i one has a 1/12 chance of winning it all if you are picked, so i'd wonder what are my odds of being picked and can i do anything to improve them...in fact, its maybe best to get everyone in the bar that night to agree to put in $1 and chop, +ev for all because of the carryover

I mean whatever is left I'm not worried. I am just wondering the odds to not have it picked so far as bizarre as that might be mainly because of a discussion I had with a few people on it who thought it was way worse odds then about 15% for this to happen. They aren't math people at all but it just had me thinking what the approximate odds were.

As for the drawing itself yes it's like a lottery as they are probably selling 60k+ tickets alone next week which they dump the tickets that were bought the previous week each time but still. Nah, obv don't expect to win as I'm not a lottery person in general even though this is way more +EV to hit for 400k+ versus any state lotto type of shit. Someone will hit this soon. The bar is drawing way more traffic from people who never would walk in to go eat and drink then ever before just because they are there to buy a few tickets for the charity which the bar gets jack shit from but it's all this added business because of this promo that they are making out on.

I'm not buying a few hundred bucks of tickets each week like some people do ($5 to $20 a week for me) as I don't do too much lottery type of gambling. As the jackpot has gone up each week I've bought a few more tickets each week as that is the scheme which works with lotteries too even though someone is guaranteed way better odds even if 60k tickets to hit this compared to any lotto out there for that kind of money. Even getting your ticket pulled don't pull the ace of hearts you still get at least $500 up to $2k depending on what card is in your envelope from the ones left.