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Multiple Raffle Strategy

Have you ever been to an event where there is a multiple raffle? The premise is simple: There are a plurality of prizes and you enter a raffle by placing your ticket into that drawing (typically a gold-fish bowl) of your choice. At the end of the evening, each drawing is performed independently. The winning ticket from each drawing gets that prize.

If there is only one prize you care about, clearly, your best strategy is to place your ticket into that drawing.

If you are agnostic as to the prize you win, your strategy should be to place your ticket into the bowl that has the lowest number of entries (Maybe waiting until just before drawing begins, and slipping your ticket into the least popular bowl?!)

Multiple Tickets

But, what if you have multiple tickets? How would your strategy change? What if the bowls are occluded and you can’t see how many entries were in each drawing (or there were sufficiently many that you could not estimate?)

Is it better to put all your eggs (tickets) into one basket (drawing), or distribute them over all the drawings?

Again, let’s make the assumption that you are agnostic as to the prize you win (because, if you only cared about one, and only one, of the prizes you would still put all your tickets into that drawing).

The question comes down to the tradeoff: Does having more ‘skin in the game’ (multiple chances in one drawing), outweigh having multiple attempts at winning prize. Let’s take a look.

Let’s assume there are N tickets in the lottery before you place in your tickets.

Let’s assume there are d parallel drawings (competitions to enter).

Let’s assume that you have t tickets to distribute.

As we have no other information to go on, let’s assume that the existing entries have been uniformly distributed through the drawings. So, before you determine what to do, the N tickets have been spread through the d bowls so that each bowl holds N/d tickets.

All eggs in one basket strategy

If you place all t of your tickets into one drawing, the probability of you winning is:

This is a simple calcuation. Before you added your tickets, there were N/d tickets in the bowl. You’ve just added t more, so now the total number of tickets in the bowl is t+(N/d). Out of these, t tickets will cause you to win the prize.

Let’s put some real numbers in there. Let’s imagine there are 1,000 other tickets out there (N=1,000), and that there are five raffles (d=5), and that you have five tickets (t=5).

If you place all your tickets in the same bowl, your chance of winning is 5/(5+(1000/5)) = 5/205 ≈ 2.439%

If you had ten tickets, your odds increase to 10/(10+(1000/5)) = 10/210 ≈ 4.762%, not quite double.

Spread the love strategy

Now let’s see what happens if we distribute our tickets through all the drawings.

To calculate the probability of at least one win, we need to find the probability of losing every single drawing and subtract this from 1 (certainty). We need to do this because, with a ‘spread the love’ strategy it’s possible to win more than one of the prizes.

If you have t tickets then distributing these evenly you will be putting t/d additional tickets in each bin which, before you placed in your tickets, held N/d tickets.

You lose a drawing if your ticket is not selected, and this happens N/d times out of (N/d + t/d) times. There are the total of d drawings, so we multiply these probabilities together (logical AND), and this is the d th power:

Let’s run the same values from the example above: N=1,000; d=5; t=5

If we place one ticket in each of the five bowls, the odds of winning at least one prize is:

1-(1000/(5+1000)) 5 = 1-(1000/1005) 5 ≈ 2.463%

This is a slightly higher chance than putting all the tickets in one drawing at 2.439% (plus there is also the chance of winning more than one prize!)

In the ten ticket example, if you place two tickets in each of the drawings: N=1,000; d=5; t=10

1-(1000/(10+1000)) 5 = 1-(1000/1010) 5 ≈ 4.853% (cf. 4.762%)

The math is clear – Spread out your tickets*

With a ‘spread the love’ strategy, not only are your chances of winning anything better, you also stand a chance of winning more than one prize.

*Assuming that the other tickets are fairly evenly distributed.

Here is the data in graph format. Below are two curves showing the percentage chance of winning based on the two strategies. For both, the number of other tickets is kept constant at 1,000 and the number of parallel raffles is also kept at five. You can see that the orange line (spreading the love) is always higher than the blue line (putting all tickets in one drawing). Also, remember that by spreading your tickets out there is a chance that you may win more than one prize!

Multi-armed Bandit

There is a related, and more complex, problem in probability theory and this is given the name of the Multi-armed bandit problem. I’m hoping this will be a topic of a future blog post.

In the multi-armed bandit problem, you are standing in front of a row of slot machines. Each of these machines has a different payout probability. You are given a finite number of coins to bet, and your goal is to maximize the return from your investment.

Herein lies the problem: Clearly you want to consistently play the machine with the best payout odds, but how do you know which that machine is?

You might get lucky, and on your first attempt, get a machine with pretty good payout odds, but how can you be sure it’s the best machine? Maybe every other machine pays out more than the machine you are currently playing? The way to find out is to try some of the others, but if you do that too much you’re wasting money playing poor machines. Also, since this is random, maybe you were just lucky on your first machine and it’s really the worst paying machine, and your early wins convinced you to keep playing? Maybe when you tested one of the other machines to see how lose/tight it was, you were just unlucky and the best paying machine did not pay you when you sampled it.

Clearly some strategy similar to the Sultan’s Wife problem is in order (also sometimes called the dating problem, or the secretary puzzle …) in which you spend some time sampling each of the offerings to build in idea of the range of the machines, and then focus your efforts on the higher paying machines. If the sampling period is too short then you don’t get a good estimate of the expected output of the machines, but if you make the sampling period too long, then you don’t have adequate time to capitalize on what you’ve learned as you’ve wasted too many bets finding the better machines.

Where the multi-armed bandit differs from the secretary style puzzles is that it is dynamic; as you go along the odds are continuing to change. With every bet you are learning more about the system. You might start off thinking that one machine is the better machine, but after a while, your results might cause you to churn from this as you play it and your average winnings start to fall.

The multi-armed bandit has great applications in rapid product development where multivariate tests need to be run (such as web pages, feature sets, or pricing models). With a live service you want to maximize some parameter (revenue, engagement, trust …) at the same time as operating it. Many great papers have been written about this problem.

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Multiple Raffle Strategy Have you ever been to an event where there is a multiple raffle? The premise is simple: There are a plurality of prizes and you enter a raffle by placing your ticket into

How to Win a Basket Raffle Without Cheating

Jamie is a student of physics, mathematics, and philosophy who enjoys raffles, among other things.

A roll of raffle tickets.

Ever fork out ten bucks for a raffle and have some old lady beat you after only investing a quarter? I have, and it was ridiculously annoying. Imagine seeing a bucket filled almost entirely with your name deliver the only ticket not yours. Unlikely, right? After all, percentages and randomness determine a raffle, right?

WRONG! Certain factors skew the randomness, making the conventional raffle more of a strategy game than a game of chance. Here are some tricks on how to win that basket raffle and why they should work for you.

  1. Be Patient
  2. Disperse Your Resources
  3. Choose Your Basket Raffles Carefully
  4. Pick Your Battles
  5. Crumple Your Ticket
  6. Don’t Leave!

A basket raffle.

1. Be Patient

Patience is the key to success. Sometimes when the tickets are being drawn, a person merely spins the tickets around and picks one off the top. This inefficient mixing method doesn’t actually mix the tickets at all. It just rotates the tickets in the bucket a few times, which makes whichever one is on top more likely to be drawn. So if you’re only going to buy a ticket or two, you might want to wait towards the end of the selling period. You’ll be that much more likely to win the raffle if this is the case.

2. Disperse Your Resources

Just like in the above method, inefficient mixing methods can very easily skew randomness. So what if the person drawing the tickets doesn’t thoroughly mix and simply moves clumps around? In that case, your huge stack of tickets might all be on the very bottom. In order to avoid this, try buying periodically throughout the buying window. That way, you know you’ll always have a chance in every raffle regardless of how the tickets are mixed.

3. Choose Your Basket Raffles Carefully

Sometimes, despite the basket of crap being full of things you’ll never use, it might actually contain something valuable to someone else. For instance, everyone for some reason attempts to win the basket raffle with chocolates and other sweets. Looking at the monetary value of the contents, it’s usually barely worth putting a single ticket into these baskets.

Some crappy hair product basket, on the other hand, might have some reasonably expensive formulas. Hair product is expensive! Also if you ever see a ticket basket for the most part empty, try to win that one, regardless of whether you want it or not. At least you’ll win one of the raffles.

Raffles can be serious business.

4. Pick Your Battles

Obviously, a bucket filled to the brim with tickets is going to provide little opportunity for success. If the tickets sold strongly outweigh the cost of the basket, then the raffle was a success for those hosting it, making it a lost cause for you. It’s just like playing the lottery. You’re more likely to spend the total jackpot before you win it, so the practicality in playing is greatly diminished.

On the other hand, the cause might make buying a ticket worth it, or maybe just the thrill of gambling. If you want to be a good person or have a good time with it, just try dispersing.

Crumpled paper sticks out in a basket full of tickets.

5. Crumple Your Ticket

Your ticket will take up more volume and stand out among the crowd if you crumple it a bit before putting it in the basket. The person pulling the raffle might glide their hand against all of the smooth surfaces and catch yours. I’ve tested this one, and I’ve got to say, I felt a little bit ashamed for it. It almost always works. Don’t make it too obvious you’re doing it, though. It’ll look suspicious, and someone might realize it. Just be inconspicuous and don’t crumple it too much.

6. Don’t Leave!

I’ve been around for many raffles in which someone just isn’t there to claim the prize. Don’t expect the drawing to occur before you go. In reality, those tickets aren’t being drawn until the very last minute, in most cases. If you’re going to put out the money, at least give yourself a chance to win the raffle.

This article is accurate and true to the best of the author’s knowledge. Content is for informational or entertainment purposes only and does not substitute for personal counsel or professional advice in business, financial, legal, or technical matters.

Comments

triston on March 06, 2020:

I want to win a nintendo switch

EMMA on January 16, 2020:

I HAVE TO WIN NOW CAMERON .

Kristin on December 13, 2019:

I didint win anything but i hope i get chance to win and it will help

Malake on December 05, 2019:

Instead of crumpling you should make a little rip too so they can get the fingers stuck and they will pick yours! thank u i just won a lot of money a electronics and a house!

Lindsey on June 01, 2019:

i need to know this stuff thx

junita on May 13, 2019:

I HOPE THIS WORKS.

ANDRES on March 23, 2018:

GOING TO HAVE A RAFFLE SOON TRYING THESE METHODS I HAVE 23 TICKETS

Hinata on March 06, 2018:

I entered in a raffle several times, I couldn’t put it at the top because whoever turns it last has to pay extra. And your not allowedto crumple them. So sorry, but this method doesn’t work for me. Is there another way?

Lawrence Cotnam on December 05, 2017:

Learned this trick years ago. Entered a multiple prize contest with nine tickets and won seven prizes My wife has won several times and I won a prize this weekend. Please delete your article and keep this a secret. (Just kidding)

Chuck on November 04, 2017:

I tried this but rather than crumpling I just bent it and I won a ratchet set worth $95!! Thanks!

pancho pantera on July 17, 2017:

thanks for your advice! very useful. Let you know if I win

Jimbob Bob on March 22, 2017:

i here that the crumpled one works well hope to try it soon.

Jimbob Bob on March 22, 2017:

Haven’t tried any yet but at my school we have Literacy baskets for MARCH and can’t wait to try 1 of the many techniques.

turok on December 05, 2016:

What about a revers draw?

jp33 on November 17, 2016:

i have a school raffle tomorrow and i will try these and hope to win

Tim on August 06, 2016:

Isn’t crumpling your ticket manipulating the draw and basically cheating?

G on July 16, 2016:

Use the “patience is the key” and “crumple the sucker” methods together. It works great!

Jessica on September 24, 2015:

Okay, this is amazing. I won $1,000 out of at least 1,000 THS IS A LIFE SAVER

I am so glad I looked this up, because heck, I JUST WON IT

Thank you so much and please keep posting more.

almost cheating on March 22, 2015:

The last few raffles ive gone too have been crazy. i started crumpling. more or less just folding the ticket to put a bend in it. Ive never won so much stuff. People are amazed. and so am I.

J on October 29, 2014:

Just used the crumple. I won 1 of 2 iPads out of a group of about 180 people ! Nice strategy

Darlene on November 15, 2013:

I have always used the crumple method. It gives the ticket some texture and almost always wins. Let me give you an example of what I have won, no lie: 2009 Harley Davidson, 2013 ticket to the Victoria’s Secret Fashion Show, a miniature go cart, and other random liquor and gift baskets

Prici3x0.44 on October 27, 2013:

What are the chances of winning the raffle with all of the tricks ?

marion langley from The Study on June 29, 2013:

I am so trying this. I’ve heard of the crumple tip but the waiting for the last minute to play is genius! Thanks for writing.

Kellie on November 17, 2012:

Wow, These sounods like really good tricks especially the crumpled noe. I should try this tomorrow.

colpolbear (author) from Pennsylvania on February 06, 2012:

lol! Thank you rain.

Rain Defence from UK on February 06, 2012:

Nice one, I had never really thought of crumpling the ticket before, but yes it makes sense that it would stand out to the picker. I can just see you with a load of blue rinsed old ladies standing around the bucket, you in your suit with slicked back hair, shades and a menacing look on your face walking away with the hemorrhoid cream every time while the grannies sigh..

colpolbear (author) from Pennsylvania on January 27, 2012:

colpolbear (author) from Pennsylvania on January 27, 2012:

I have unofficially tested them. I didn’t go and make a statistical analysis or anything, but through observation and comparison, I’ve found that these all at least enhance the chance of winning. They all work relatively well but that doesn’t mean they’ll always work for you. I highlighted the crumpling method because, well. that one works ridiculously wonders.

stephaniekawula from Missouri on January 27, 2012:

Have you tested all of these tips or was it common sense?

Get some tips on how to win a raffle—without cheating! Whether it’s a basket raffle or a fifty-fifty, these tricks will improve your chances of winning tremendously.