Roulette Game in Europe

I’m going to talk to you about the type of maths I like. The type of maths I like is probability theory. My story is about my friend Daan. He likes to brag that he always wins money at the casino or playing with free spins no deposit win real money in online casinos. Allow me to explain Daan’s strategy.

Daan says that he plays roulette in the casino. With roulette, you have a table with a sectioned layout. A ball is spun, falls into a pocket… …and this pocket is either red or black, or even green.

You can bet on all kinds of things. If you bet red, you win when the ball ends up in a red pocket. If you bet black, you win when the ball ends up in a black pocket. You bet a certain amount on either red or black…and if you win, you receive double that amount.

If your stake is 1 euro, you win 2 euros, and so your profit is 1 euro. If you lose, your stake is gone. Daan’s strategy goes as follows: I go there, I keep doubling my stakes, until I win and then I stop. Let’s see what happens, because he says this is making him rich. He’s not rich, so that’s suspect in itself. Let’s see.

In the first round, his stake is 1 euro. This means that when he wins, he has a profit of 1 euro on this side. But if he loses, he’s on -1 euro. In the second round, he doubles his stake, which amounts to 2.

If he loses, 2 is subtracted from -1, and so he goes to -3. If he wins, 2 is added to -1, and so his profit is 1 euro. In the third round, his stake is 4 euros, double the previous stake of 2 euros. If he wins, 4 is added to -3, which results in 1. If he loses, he’s on -7. One more round to clearly show the pattern here.

His stake would be 8 euros. If he wins, 8 is added -7, resulting in 1. If he loses, 8 is subtracted from -7, which puts him on -15. Oh dear, there’s ink everywhere. This means… You see: as soon as Daan wins, he makes 1 euro profit.

He could just continue doing that until he’s rich. Daan’s argument is that he has to win sooner or later. He can’t just keep losing several rounds in a row. For example, one can easily play 100 rounds of roulette in a couple of hours. What are the chances of losing 100 rounds in a row? We can calculate this.

For simplicity’s sake, we’ll assume that the chance of red winning is exactly 0.5. It’s actually a bit lower. And for black it’s also 0.5, making it easier to calculate. This means that losing 100 times in a row… The chance of losing is 0.5.

Multiply that by 0.5 for losing the next round. 0.5 times 0.5 for losing twice in a row. The chance of losing three times in a row is 0.5 times 0.5 times 0.5. Losing 100 times in a row, is expressed by 0.5 to the power of 100… …which is equal to 2 to the power of -100. Or put differently: Approximately 7.8 times 10 to the power of -31.

That’s a really low number. I’ll give you an idea of how low exactly: The time the universe has existed, in seconds… …is approximately 10 to the power of 17. If you had a played a round of roulette for every second since the Big Bang… …there’s a very low probability you would’ve lost 100 times in a row. This is what Daan’s strategy is based on. Sooner or later he has to win, because losing 100 times in a row is impossible.

But as said, Daan still isn’t rich, and so there’s something wrong. Let’s calculate what Daan’s stake is in round 100. Stake…

I’m sorry, that should be total stakes. We know that the stake in round 100 is 2 to the power of 99. But we want to know the total of cumulative stakes after 100 rounds. In the first round the stake was 1 euro. We assume he plays 100 rounds.

In the second round it was 2 euros, in the third it was 4 euros… …and so on, all the way to 2 to the power of 99. Here we have 2 to the power of zero, to the power of 1, to the power of 2… …and so at round 100, it’s 2 to the power of 99. How do I add all of this? I’m applying a trick, as mathematicians are wont to do.

I’m going to multiply by 1. That sounds as if nothing will change, but you have to do it the smart way. In this case, you multiply with 2 minus 1. So, it’s 2 minus 1, times 1 plus 2 plus 4, and so on… …all the way to 2 to the power of 99. What does it say?

2 times 1 is 2, 2 times 2 is 4, 2 times 4 is 8… …and 2 times 2 to the power of 99, 2 to the power of 100. Now for the -1. That’s easy.

It’s exactly the same as what we had. The big advantage of doing it this way, is that I can now cancel out numbers. 2 against 2, 4 against 4, 8 against 8… …2 to the power of 99 against 2 to the power of 99. What remains?

This number and this one. That’s 2 to the power of 100, minus 1. 2 to the power of 10 is approximately 1000. 2 to the power of 20 is around a million.

2 to the power of 30 is a billion. 2 to the power of 100 is more money than there is on the whole planet. Daan will never be able to bet such a stake.

Casinos are smart enough to say that you need to have the money you want to bet. That means that at some point the jig is up for Daan. He’s not making it to round 100… …or even to round 20, as he’s not a billionaire. Let’s say he can play M rounds, with M representing a number. That leads us to the following calculation: In round M… …his stake is 2 to the power of M minus 1.

He can do two things, either win or lose. If he wins, he gets that 1 euro profit, after all. But he can also lose.

If we perform the same calculation as this one here… …we see that his total becomes -2 to the power of M… …minus 1, or rather plus 1, because this here is already minus. What is his expected profit after M rounds? He can either lose M times in a row, and in that case…

The probability that he loses M times in a row, is 2 to the power of -M. How much will he have lost then? His profit will be negative… …and amounts to -2 to the power of M, minus 1. But he can also have won, somewhere between round 1 and round M. In that case, he has won 1 euro. What’s the probability?

It has to be 1 minus the probability that he loses M times. That’s 1 minus 2 to the power of M. Let’s write that out. It’s -1 plus 2 to the power of -M… …plus 1 minus 2 to the power of -M, and that equals zero.

So, the expected profit after M rounds, is simply zero. Which explains why Daan isn’t all that rich. You might say that Daan isn’t smart and needs to devise a better strategy. Unfortunately, that can’t be done.

In a masters class I teach, we prove the following statement: If you play a betting game… …where your expected profit without a strategy is zero… …the expected profit after M rounds with a strategy will also be zero. Likewise, if the expected profit is negative, which it is in a casino… …the expected profit after M rounds with a strategy will also be negative. Does this mean it doesn’t matter whether you use a strategy in the casino or not? It depends on how you look at it.

You can do interesting stuff with a strategy. For instance, you can play with 32 people on the same roulette table. 32 equals 2 to the power of 5.

That allows you to cover all possible outcomes of 5 rounds of roulette… …ignoring the green pocket. That means person 1 bets on red five times in a row. Person 2 bets on red four times in a row, and then black.

Person 3 bets on red three times in a row, then black and then red. Person 4 bets on red three times in a row, then black and black again. You do this with all 32 persons, to cover all possibilities. This means that after those 5 rounds… …one of those 32 people will have won 5 times, and one will have lost 5 times. If everyone hadn’t agreed to do this… …the probability that one of those 32 people wins 5 times in a row… …would’ve been smaller than 1 divided by E, which is smaller than half… …or smaller than 1, either way. So, for a group with a strategy, the large ups and downs… …the largest profits and losses within that group… …are potentially larger than those of a group with no strategy.

It’s not a coincidence that I’m telling you about this. This is related to the research I’m doing. In my research, I look at models for systems… …that are characterized by arbitrariness in many spots. For example, an emulsion of oil droplets in water. Those droplets aren’t perfectly round. The edges are somewhat arbitrary, going every which way.

Shares are another example. If you look at share prices, you don’t see straight lines… …but rather, they seem to be going up and down arbitrarily. Often, the average size of such a wobble… …of such an arbitrary step, depends on the state of the system. If I look at a share price and it’s very high… …the average jumps will be larger… …than when the price is low. One interpretation is that the share has a gambling strategy. What happens, depends on the state you’re in.

It’s quite difficult to analyse. What we’d like to understand… …is whether one can compare such a system with a system with no strategy… …where the rate of change doesn’t depend on the state you’re in. This kind of questions are related to that. If you enjoyed this and want to know more about maths… …check out our study programme at the University of Amsterdam… …via the link below. Maybe we’ll see each other in class.

want to know more? visit uva.nl/wiskunde

RVing in Key West for Lobsterfest 2018

It is Friday, August 10th, 2018. And today, we’re going back to Key West. ‘Cause it is, once again, Lobsterfest. (upbeat salsa music) You might say, Key West, again? But, believe it or not, there are a bunch of things in Key West we haven’t done, yet.

You’ll see. Hm, no tiki bar, yet, in the Postcard Inn, since it got blown over by Hurricane Irma. So, anyways, the idea is to see some of the stuff we haven’t seen yet, and revisit some of our all-time favorites. (upbeat tropical music) Sunshine Key, here, looks like it is almost ready for the high season. Yeah, that one suffered pretty heavy damage from the hurricane, too. Well, here we are, Boyd’s Campground on Stock Island.

This is our site, here. It’s horribly hot. Anyways. Greetings from paradise. It looks like there is some activity, here, at nearby Boca Chica Naval Air Station.

Very cool to see it. It is almost like an air show, and I love planes. Although, I probably shouldn’t be flying the drone today. Just in case.

By the way, where we are, here, Stock Island, is the Key just before Key West, so we could almost walk over there, if we really wanted to, but it is hot and muggy, and, luckily, now they have Uber and Lyft, here in Key West. So we’re probably gonna do that, especially after an IPA. The campground, full of iguanas. Well, we’re gonna take a Lyft down to Key West, because we don’t really feel like driving, and we might consume a couple of adult beverages along the way, so that’s what we’re doing. And it looks like we have a new welcome sign in Key West. Our Uber driver, Key West native, super-friendly.

She seems to know everybody out on the street. Now, crossing Duval Street. And here we are. First Flight Brewery.

It was here, that the now defunct Pan American Airlines began operations in 1927, as a sea plane service to Havana. Scallops and hummus. Well, we just had some appetizers, here at the First Flight Island Restaurant and Brewery.

And this happens to be, I mean, and they should trim this tree, but this is the birthplace of Pan American Airlines. And I just did a live video from here, by the way. Very cool, very cool to get your interaction, and now, we’re gonna go to Duval Street, see what’s going on, because, you know, we’re in Key West. This is The Southernmost Microbrewery. Very cool.

This is Historic Captain George Carey’s House, dating back to 1834. It is the second oldest house in Key West. It’s for sale, if you guys want to buy it. I’m sure they’re asking, it’s a deal, I’m sure it’s a deal.

And Key West is, of course, famous for it’s unusual, peculiar apparel. Well, we haven’t been to Sloppy Joe’s in quite awhile, so let’s check it out. And, by the way, there is live music, here, everywhere. Here we are, Sloppy Joe’s.

– I saw him live two years ago, and women were still throwing panties at him, okay? Tom Jones, you’ve still got it goin’ on. – [Robert] I’m sorry to say it, but it is one of the worst Mojitos we’ve had in awhile. And I even think the plastic cup is supposed to be a collectible. I’m sorry, but I tell it like it is.

Talking about places we’ve never visited, and there’s the former customs office, which used to have a huge sculpture up front. Not anymore. The Shipwreck Museum Tower, and the Aquarium, of course. We’ll visit those one of these days.

Hello there. Don’t be afraid. As we approach El Meson de Pepe, we bump into Mark Schultz, and his wife, and they own the Suite Dreams Inn, here in Key West. It is a boutique guest house, and I look forward to visiting one of these days. Here we are, El Meson de Pepe. (“Smooth” by Santana) (upbeat salsa music) We couldn’t get a seat at the bar, so we just took two Mojitos, to go.

And then, came to Mallory Square, here, to witness the sunset. There’s the local mermaid. And the live music.

I guess, because there is a little fog or humidity in the atmosphere. That, in front of us, is the very aptly named Sunset Key, because the sun usually sets right behind it. Well, that was a unique sunset, here in Key West. They’re all different, but this one was particularly interesting because the sun wasn’t very bright, because there’s a lot of moisture in the atmosphere. (upbeat salsa music) Here’s a curious shipwreck, named Mary. As night falls, we are making our way back to Duval Street.

Ooh, a winery in Key West! Tropical Wines. Key West’s First Legal Rum Distillery. Hm, let’s check it out! Yep, let’s do a tasting.

That’s where they make the rum. Pretty cool. And this one has a particular flavor, because when they were aging it, Hurricane Irma came in and because of the heat, or something like that, it got a special caramelized flavor. So I’m gonna taste it. This is the competition.

Maybe we’ll come here tomorrow, maybe. We’re gonna have dinner, here at B.O. ‘s Fish Wagon. Ooh, so hot. But B.O. Fish Wagon, we’ve actually been meaning to come here since, at least, a couple of years ago.

And the sandwich, it doesn’t look like much when you get it, but it was delicious. It looks like Pepe’s lost its original sign during the hurricane, and they haven’t replaced it, yet. By the way, great Mojitos here, with a great local vibe. Although, not today. Like almost everywhere else, business seems to be slow. Anyways, good night.

And good morning, from Boyd’s Campground. We got a friendly iguana, here. Ooh, it’s a swimming iguana! I have seen many iguanas in my time, but never seen one swimming.

And now it’s raining. Gotta love that unpredictable South Florida summer weather. You like it here, don’t you? And that’s our neighbor, the iguana. Here at Boyd’s. Right outside our door.

That’s why, that’s probably why it’s still a little… This is still early for Lobsterfest. So let’s go to Margaritaville, instead. We can always have breakfast, or brunch, or early lunch, here at Jimmy Buffett’s place. Some people have Mimosas for brunch, we have IPAs.

And the crab asiago dip. Yum! Yeah, they make you walk a long way to the restrooms. They even have mile markers.

(air dryer whirring) Well, there we had breakfast at Margaritaville. Let’s go see the lighthouse, we’ve never been there. And it is starting to get, actually, a little busy, right now. The San Carlos, here, is a very important building in Cuban history. It is where the Cuban exiles, back in the 1870s, planned the Campaign of Independence from Spain.

We might visit later. Okay, this is different. Here’s the Green Parrot, which dates back to 1890. I’m telling you, sometimes I think Key West has always been a party town.

There’s an old wooden church. The Cornish Memorial Zion Church. One of these days, we are also going to take the Conch Train, but not today. I love those old Toyota-based Class C motor homes. The Winnebago Warrior, perhaps.

Hm, what is this place? I had never seen it before. Although, apparently it is a very historic neighborhood, here.

You see, Key West always has surprises. Even after all these years. There is Hemingway’s house, of course. But we’ve been there, done that.

Actually, we were going a little further down the street to the Key West Lighthouse. The Key West Lighthouse. Here, they have the Fresnell lenses, very cool. And even cooler, all these chickens, out here! And there’s the lighthouse.

We’ve never actually been here before. And it is a long way up. Well, this was one of the few places we had left, here in Key West, we hadn’t seen.

Everything looks kind of different from up here. Down there, it’s Hemingway’s house, and in the distance, Mount Trashmore, a former landfill, and the highest point in the Florida Keys. (soft relaxing music) It doesn’t say anything, but um… Might not be safe.

All right, let’s go back down. It’s very nice up here. Maybe a little bit of a stretch for 10 bucks. Eh, but we’re in Key West. Hello, there. You don’t say much, do you?

Well, we made it. It’s incredibly hot, here in Key West. Not only hot, but incredibly humid, so you sweat a lot. There is, of course, a museum. Lighthouse Keeper Parlor. I’ll let you in on a little secret.

We came in as much for the history, as for the air conditioner. Ah, does it feel nice in here. And there are Fresnell lenses. An Ibis Bird. Let’s continue our exploration of Key West.

It’s a Roadtrek, a 190 Popular. Here we are, leisurely walking on Whitehead Street. There’s the Monroe County Courthouse. Mile Marker 0 of US1 one should be close by. And here we are, at the beginning.

And the end. The alpha, or the omega, depending which way you’re going. Hopefully, soon I’ll be able to show you the other end, up in Maine. The street fair, here, much more animated, now that it is later, and the weather is holding up. Key West’s oldest house has opened up its backyard for people to come and sit down, but I guess not many people know about it.

And besides, it’s too hot to be sitting in the sun, anyways. And this is The Oldest House, I’m assuming, over there. This time around, prices seem slightly higher than in previous years. And the lines are equally long.

And here, we bumped into Katrina, viewer of the channel. And also, Nelson and his wife. Always makes my day to meet people in the street, who watch my videos. (upbeat salsa music) The Lobster Roll Challenge. We did that last time we were here.

That is a Maine Lobster Roll versus the Florida Lobster Roll. By the way, two totally different animals. Let’s begin with the cheapest option, here, which is the half lobster tail on a stick, for $10. (upbeat salsa music) Next, we’re having the $24 platter with an extra tail for 16, for a grand total of 40 bucks. Really delicious, and cooked to perfection.

Last, but not least, Willie T’s Full Tail Dinner, for $26. It looks great on top of the grill, but the final product, a little overcooked, and not the greatest flavor. Remember I mentioned the San Carlos, earlier? Well, it is open, now, so let’s check it out. They have old magazines and this stamp exhibition. Even old Cuban money from the 1950s.

Lots of memorabilia. It was here, in Key West, that Cuba’s greatest hero, Jose Marti, planned the War of Independence from Spain, which began in 1895. He also went to Ybor City, in Tampa. Unfortunately, he was a leader and a writer, but not a fighter, and got killed, pretty much, in the first battle of the war. They have some pretty rare photos of him. Also rare, a phone book from 1958, and guess what I found?

My childhood home address and phone number, under my dad’s name. That’s super cool. Well, let’s go upstairs since we’re here. By the way, I don’t think they have air conditioning in here. There, all the presidents of Cuba, before the Castros.

A raft used to flee the island, probably from the mid 90s. And that old typewriter. Presumably, Marti’s library. There is AC, but it doesn’t look like it’s working very well.

Anyways, after this pause let’s continue exploring Key West. Okay, the San Carlos was a nice break. And the verdict, the first lobster was too small.

The third lobster was too hard. The second lobster was fantastic. This here, is the line to take a picture with the southernmost point in the Continental United States, right there. Oh, yeah, we’re not gonna do it today. Been there, done that. It’s a cool thing if you’re here.

There’s always, lately, there’s always a line. Southernmost house. Of course, we’ve been here many, many times. But next, we are walking towards an area of Key West that either we’ve never been to, or it’s been a long time.

There’s an oldie. Another Toyota. It’s either a Dolphin or a Brave.

Could be a Minnie or a Warrior, as well. Well, here’s a little playita. This area of Key West, which, actually, never explored before. It’s pretty cool.

There’s the Dog Beach. Look at the pelican. Fly, pelican! Oh, he flew.

Almost. Key West, here, definitely not known for its white, sandy beaches, that’s for sure. Casa Marina. This Casa Marina, very big and ritzy beachfront resort.

And here we have Higgs Beach. There’s some hurricane damage still visible in this area. These red brick ruins, here, are the West Martello Tower, which, unfortunately, is closed by now. It is what remains of a 19th Century fort.

And the grounds inside are supposed to be really pretty. Here’s the site of a recently discovered slave cemetery, dating back to 1860. African Cemetery. They actually discovered it by using an underground radar. There’s also an AIDS memorial, dedicated to the lives touched by AIDS. And there’s also this long pier, let’s check it out.

Towards this area to the east, there’s a bunch of hotels and condominiums. Pretty typical. There’s a bunch of people fishing.

There seems to be, like, a jet ski tour, and that looks like it could be a lot of fun. There are a couple of gentlemen here, from the Florida Fish and Wildlife Conservation Commission, inspecting the lobsters some of the people are catching. But I don’t feel comfortable filming them, so no video. You know, bothering the local wildlife here, can be a lot of fun, but we are totally exhausted. We’ve walked many miles today.

Six and a half, according to my Fitbit. So let’s go back to the campground and rest, because tomorrow we are going snorkeling! And I was totally kidding about bothering the local wildlife. I don’t do that.

(relaxing music) Shortly after returning to the campground, we got a surprise visit by some viewers from Germany. They’re staying a couple of sites over. Well, here we are, back at the campground. It rained quite a bit.

I think we’re gonna see the sunset from here. Very pretty. (relaxing music) There was supposed to be a meteor shower tonight.

The Perseid, but all we got to see was some lightning, and then, it got cloudy. Well, good morning. It’s warm and muggy. As we await the sunrise.

And here we are! Fun fact, if you look it up in a map, this is actually the southernmost beach in the island of Key West. And there is a cruise ship coming over the horizon.

Proof that the Earth is not flat. This is also, probably, the best natural beach, here in Key West. Which, as I mentioned earlier, is not known for it’s white, sandy beaches. So this is, pretty much, as good as it gets. Right here, where the Atlantic meets the Gulf of Mexico.

Let’s go snorkeling around these rock formations. Well, I’m having a great time, here in the salty water. It is, as you can see, not a very sandy beach, so water shoes are, pretty much, required.

Still very enjoyable. I guess this area belongs to the Naval Air Station, and the No Trespassing sign, it goes both ways. (peaceful upbeat music) This looks like another nice area to snorkel. Just watch out for the birds, I guess. Unfortunately, it is getting a little murky.

Still, lots of fish There comes the big boat. It is the Majesty of the Seas.

About 26 years old, but still very majestic. How about an IPA, here at the Cayo Hueso Cafe? Cayo Hueso, by the way, means bone key, in Spanish. And the name of the island when all this used to belong to Spain. 105 miles to Havana, all right, there. Overall, very nice state park.

Lots of picnic tables, and lounge chairs for rent. And I believe it is the first state park that I’ve been to where they, not only allow, but sell alcoholic beverages, but, then again, you’re in Key West. Boy, am I glad we came early.

It is getting really crowded, now. By the way, there is RV parking, if you want to spend the day here. Just no overnight.  Look at the line of cars coming in, now. We’re gonna go back to the RV, take a break, shower, and then come back for lunch. Look at it, La Pensione.

We stayed there once, many, many years ago. (upbeat tropical music) A group of young people arrived this morning with all these green tents. It almost looks like a refugee camp. We enjoy the nearly empty pool.

And the local wildlife. And a bunch of people have recommended El Siboney, so let’s check it out. Cuban bread, and a sunset ale to begin. Ili got the the Sangria. And I got the lechon. You know, pork roast.

And the fried pork chunks, which is my favorite. Okay, El Siboney, this place came highly recommended by several people, and it’s fine. It’s hard to mess up lechon, or fried pork chunks. It’s fine, it wasn’t bad, but, I mean, they have more cameras in there, per square foot, than in Las Vegas casino. And the employees seemed so miserable.

And it’s kind of out of the way, in this neighborhood, here. So, I mean, if you have to have your lechon fix, by all means, come here. But it’s fine, it’s not great, it’s just fine. That’s my opinion.

All right, we’re walking towards Duval Street. Along this very non-touristy neighborhood, here. The never ending conundrum, why did the chicken cross the road? Is that the Denny’s where Eric Jacobs ate when he was here? This time around, I’ve seen many of these signs. Hm, troubling.

A refreshing Sangria, perhaps, on this hot day? Of course! Cool bar, by the way. Cool, art, to go.

It is kind of like a mobile art gallery, pretty cool. There is definitely an economic downturn, here in the Conch Republic. Here’s, once again, The Oldest House. The Oldest House in South Florida.

It’s been kind of quiet today. But it is a Sunday, and I don’t think we’ve ever spent a Sunday here, before. We’re making our way to Mallory Square, slowly, no rush. Although, I don’t think we’re going to wait for the sunset today.

Anyways, as we wind down our weekend escapade here, we visited some new places, did something new, you know, snorkeled, and, of course, visited some of our old favorites. And that was the plan from the beginning. By the way, for years, I had a recurring dream with this building, and I didn’t know where it was, until I came back to Key West.

This ruins, here, they look very historic, but I have no idea what they are. There’s the Sunset Pier, which was destroyed by Hurricane Irma, and it hasn’t been rebuilt, yet. And there’s a nice balcony to see the sunset from.

(guitar music) Sunset, coming soon. Well, greetings, from Mallory Square. This is not quite the conclusion, but some conclusions that I’ve gotten from this trip. Lobsterfest wasn’t as great this year, as in years past. Or, the one time I saw it in the past. Everything, prices for everything in Key West, seem to have, at least, increased by 50%.

And maybe it’s Hurricane Irma. I mean, a lot of places, not a lot, but many places, are out of business, you know, for sale, that were thriving businesses, before. So I’m sure Hurricane Irma has something to blame for that. I mean, Key West is still its charming self, but, yeah, it’s become a little more expensive than the past couple of years.

Anyways, the sunset is coming up soon, here. We’ve got some street performers here, in Mallory Square. And, by the way, it’s August, it’s incredibly hot out here. But I’ve really had a great time, as always. Whoa, I get dizzy just looking at that bird. Mallory Square, today, a kind of different vibe, compared to Friday.

I turned 72 this year. Don’t ever stop doing what you love to do. I want to dedicate the rest of tonight’s show to Ryan Barnett, my chiropractor.

Time to go! By the way, if you haven’t, make sure to check out my Key West playlist on YouTube, for many, many more videos of the Conch Republic. As always, thank you, so much, for watching, and see you on the road!