Pull tabs odds

Hello,
As you may or may not know, pull tabs are a very popular gambling game in Minnesota. Usually tickets are thrown into a box and the big winner tickets have a board where they get crossed off as they are won. In a few places they have machines which you stick money in and get tickets and turn winners into a real person (usually a bartender). The machines have lines that tell you how many tickets are left, where the boxes you have to guesstimate. Today I was in a bar and looked at the machine. it had around 985ish tickets and 10 big winners left totaling 825 bucks at 1 buck per ticket. So I figure if the very last ticket is a big winner and I have to buy them all to recoup my losses I'd be down a maximum of 150ish bucks. I figured that was great odds considering how many tickets per winners there usually are, and what are the odds of most of the winners being at the bottom, I should go positive in money at some point and then I'd quit while I was ahead. I ended up spending 200 bucks and winning 250 leaving the box with about 800 tickets, 575 in big winners spread across 7 tickets when I got kicked out at closing time. Now I figure if I had to buy every last ticket I'd be down at max 200 bucks.


But what I cant figure out is what are the odds I'd actually go down in money. what are the odds that the tickets are close to the very end of the machine. Theres a chance I could spend 100 and pull all the remaining big winning tickets and be up a lot of money, or theres a chance all the big winning tickets could be in the last 100 and I could be down a potential lot of money depending on the box. in the scenario above with 800 tickets and 7 big winners thats 1 in 115 tickets is a big winner. I just cant help but think I could get lucky with all the big winners being close to the top or get screwed with them being at the very bottom.

I'd think that figuring out odds for a case like this would also apply to your odds at winning raffles.

Quote: pulltabjunkie

Hello,
As you may or may not know, pull tabs are a very popular gambling game in Minnesota. Usually tickets are thrown into a box and the big winner tickets have a board where they get crossed off as they are won. In a few places they have machines which you stick money in and get tickets and turn winners into a real person (usually a bartender). The machines have lines that tell you how many tickets are left, where the boxes you have to guesstimate. Today I was in a bar and looked at the machine. it had around 985ish tickets and 10 big winners left totaling 825 bucks at 1 buck per ticket. So I figure if the very last ticket is a big winner and I have to buy them all to recoup my losses I'd be down a maximum of 150ish bucks. I figured that was great odds considering how many tickets per winners there usually are, and what are the odds of most of the winners being at the bottom, I should go positive in money at some point and then I'd quit while I was ahead. I ended up spending 200 bucks and winning 250 leaving the box with about 800 tickets, 575 in big winners spread across 7 tickets when I got kicked out at closing time. Now I figure if I had to buy every last ticket I'd be down at max 200 bucks.


But what I cant figure out is what are the odds I'd actually go down in money. what are the odds that the tickets are close to the very end of the machine. Theres a chance I could spend 100 and pull all the remaining big winning tickets and be up a lot of money, or theres a chance all the big winning tickets could be in the last 100 and I could be down a potential lot of money depending on the box. in the scenario above with 800 tickets and 7 big winners thats 1 in 115 tickets is a big winner. I just cant help but think I could get lucky with all the big winners being close to the top or get screwed with them being at the very bottom.

I'd think that figuring out odds for a case like this would also apply to your odds at winning raffles.

I don't know anything about pull tabs other than what we have at local fairs. The problem that I could see is that there are 7 big winners left ONLY if they have all been cashed in already AND the people keeping track accurately report what is left. How do you know the winners? Is it someone writing it on a board or something? If so, there would be a benefit to a proprietor to lie about how many are left to entice people to spend more money. Then if someone buys them all they could just say, someone must not have cashed them out when they won.

Again, I know nothing about this system but these thoughts are the first thing that comes to mind. Other smarter people will be around to help with the actual math. It will look something like 10/985*9/984*N/Q which is way beyond my math skills. I am good with 9x16.

Quote: GWAE

I don't know anything about pull tabs other than what we have at local fairs. The problem that I could see is that there are 7 big winners left ONLY if they have all been cashed in already AND the people keeping track accurately report what is left. How do you know the winners? Is it someone writing it on a board or something? If so, there would be a benefit to a proprietor to lie about how many are left to entice people to spend more money. Then if someone buys them all they could just say, someone must not have cashed them out when they won.

Again, I know nothing about this system but these thoughts are the first thing that comes to mind. Other smarter people will be around to help with the actual math. It will look something like 10/985*9/984*N/Q which is way beyond my math skills. I am good with 9x16.

I'm not sure if you can take them home. I'm not sure how it works on the split with the bars so it may not matter if there's winners or not. Usually there's many different pull tab options to choose from in case all the big winners are gone.

Don't forget that there are other, smaller prizes available which probably makes it a positive expectation, even if you just go ahead and buy them all.


But GWAE has point. How do you know the info is accurate?

Quote: pulltabjunkie

Hello,
As you may or may not know, pull tabs are a very popular gambling game in Minnesota. Usually tickets are thrown into a box and the big winner tickets have a board where they get crossed off as they are won. In a few places they have machines which you stick money in and get tickets and turn winners into a real person (usually a bartender). The machines have lines that tell you how many tickets are left, where the boxes you have to guesstimate. Today I was in a bar and looked at the machine. it had around 985ish tickets and 10 big winners left totaling 825 bucks at 1 buck per ticket. So I figure if the very last ticket is a big winner and I have to buy them all to recoup my losses I'd be down a maximum of 150ish bucks. I figured that was great odds considering how many tickets per winners there usually are, and what are the odds of most of the winners being at the bottom, I should go positive in money at some point and then I'd quit while I was ahead. I ended up spending 200 bucks and winning 250 leaving the box with about 800 tickets, 575 in big winners spread across 7 tickets when I got kicked out at closing time. Now I figure if I had to buy every last ticket I'd be down at max 200 bucks.

That assumes that the information concerning how many of each winning ticket was in the machine when it was stocked is accurate. Things like pull tabs and punchboards are notorious for having one or more of the winning tickets removed in advance.

Where does the bar get the tickets from? What is the bartender's / bar owner's cut? How legal is this sort of thing in Minnesota? ("Popular" and "legal" can be two different things - football parlay cards are "popular" in California.)

As for odds, you would have to know exactly how many of each value of ticket (including losing tickets) were remaining.

https://wizardofodds.com/games/pull-tabs/

I'm on the run, no mention of the wizards page so I thought I'd link it.

Quote: ThatDonGuy

Where does the bar get the tickets from? What is the bartender's / bar owner's cut? How legal is this sort of thing in Minnesota? ("Popular" and "legal" can be two different things - football parlay cards are "popular" in California.)

http://en.wikipedia.org/wiki/Pull-tab - if you can trust Wikipedia, it's legal in Minnesota. (See "Jar Bars") According to Minnesota's gaming control board, pull-tabs are one of the 5 legal forms of gambling. http://mn.gov/gcb/PDF_Files/LGM%20Chapt%205%20Pull-Tabs%202014.pdf

Lottery ticket retailers seem to get between a 5%-7% cut of that price. I'm assuming pull-tabs are more. We don't care what the bar's cut is; we care what the overall RTP is - the total of all prizes over the number of tickets in a deal (times the ticket price).

Quote: Dieter

Lottery ticket retailers seem to get between a 5%-7% cut of that price. I'm assuming pull-tabs are more. We don't care what the bar's cut is; we care what the overall RTP is - the total of all prizes over the number of tickets in a deal (times the ticket price).

The bar's cut is important only in that if it is small, then it's more likely that the game could be rigged.

I will assume that a "pull tab" machine works on the same principle as the scratch-off ticket machines I see in supermarkets here in California - with one very significant difference; in a pull-tab machine, the number of prizes in that particular machine is known.

If the number of prizes won up to a particular point is known, then it is in everybody's (except the players') best interest to keep at least one large prize near the "bottom of the pile" - but if somebody can control that, then they can control how many winners are actually in that pile at the start (as opposed to how many are supposed to be there). Remember what happened with McDonald's and its Monopoly game (where the only winner turned out to be St. Jude Children's Hospital when one of the cheaters had a moment of conscience).

If you don't know exactly how many tabs are left and how many of each winning amount remains, then there's no way of knowing with any degree of certainty what the expected return is - unless you assume that any particular tab could be anywhere in the pile, in which case it doesn't matter when you buy one.

I seem to remember a electronic display (real tabs came out )pull tab machine in washington and it had a progressive. You could easily count what was left. it displayed the winners. I didn't have much time to look at it or get details. But I always wondered if you could buy them all out at a certain point and lock up a profit.

I noticed a few bars had an elaborate pull tab setup(no progressives) with about 20 different batches to choose from. They were kept scattered in clear plastic rectangular drawing drum containers behind the bar on shelves, they took up half the wall. People had big piles of discarded tabs sitting in front of them while they ripped though new tabs as fast as they could buy them. When in Rome....My 40 bucks didn't turn out so well. I was thinking to myself, they probably only return 25%. somebody probably has a cheating method, like knowing winning serial numbers, poaching them out then giving them to friends. Possibility looking under the tab or something.

There is a board where all the big winners are kept track of. Also most all places say you have to claim your winner within 15 minutes and if you go outside the tickets are void and they will not cash them. You have to go to the bartenders to cash them and all big winners you have to sign a tax form. Most bartenders will check the winners in their drawer vs what the board says to make sure it's accurate if you ask. And yes there are small winners.

I guess what I'm asking is. If you have a shoe of X amount of cards and X amount of aces. What would be the odds of distribution? What are the odds of an ace (or more) being within the first X amount of cards.

Quote: pulltabjunkie

I guess what I'm asking is. If you have a shoe of X amount of cards and X amount of aces. What would be the odds of distribution? What are the odds of an ace (or more) being within the first X amount of cards.

Let S = the number of cards in the shoe, A = the number of aces, and X = the number of cards you check.

The probability of at least one ace being in the first X cards = 1 - the probability of all of the aces being in the last (S-X) cards.

Each set of S-X cards with all A aces has (S-X-A) of the (S-A) non-aces, so there are (S-A)C(S-A-X) combinations out of a total of (S)C(S-X) combinations of S-X cards from the original S, and the solution to the original problem = 1 - (S-A)C(S-A-X) / (S)C(S-X).
((A)C(B) is the number of combinations of A things chosen B at a time; it is also expressed as combin(A,B).)

Quote: GWAE

The problem that I could see is that there are 7 big winners left ONLY if they have all been cashed in already AND the people keeping track accurately report what is left. How do you know the winners? Is it someone writing it on a board or something?

For what it's worth, in Washington, WAC 230-14-100 requires that any prizes of more than $20 be "conspicuously deleted" from the advertising sign ("flare") as the prizes are paid out. I've seen that done by either redacting them with a big black Sharpie, or placing a sticker over them (like the orange stickers on the center bin in this photo)

I'm not good with math. What does the "C" mean in the formula?

Quote: pulltabjunkie

I'm not good with math. What does the "C" mean in the formula?

You mean like (5)C(3)? It stands for "combinations" - (5)C(3) is how I write "the number of combinations of 5 things drawn 3 at a time". For example, you're playing a very small lottery, where they draw 3 numbers from the set 1, 2, 3, 4, 5. "Combinations" means that the order does not matter (i.e. 1, 2, 3 is the same combination as 2, 3, 1); "permutations" means that the order does matter (so 1, 2, 3 and 2, 3, 1 are two different "permutations"). In this case, there are 10 different combinations:
1, 2, 3 - 1, 2, 4 - 1, 2, 5 - 1, 3, 4 - 1, 3, 5
1, 4, 5 - 2, 3, 4 - 2, 3, 5 - 2, 4, 5 - 3, 4, 5
so (5)C(3) = 10.
This is also written combin(5,3), or C(5,3), or with the 5 above the 3 and a single set of parentheses surrounding them.