Last video I talked about a strategy of betting called the martingale system. It’s a strategy where you always chase the total amount you’ve lost so far by betting that loss plus 2. So that when you eventually win, you win 2 guaranteed.

A lot of you saw the flaw in this system was that the amount of money you’d need to sustain it would be infinite. The issue is, even if you have a really huge amount of money, as long as it’s finite, the expectation value from playing this game is 0. That’s because, with a very small chance, you’d run out of money to keep betting and you’d lose a lot. I didn’t believe this until I did the calculation, because it seemed like you were so unlikely to even lose many times in a row and so you didn’t really need to worry about getting to the stage where you’d need to bet big, so you didn’t have to worry about folding.

But let’s do the calculation and see what happens. Everyone has some number of losses, that would mean they will have lost enough money that they wouldn’t be able to pay the amount they need to bet for the next round, so they’d have to give up. Let’s call this number of losses for a particular person, n. n can be very high or very low, it doesn’t matter. The person only has a 1 in 2^n chance of losing the maximum n times in a row. If they don’t lose then they win 2- that’s most of the time, with a the probability (1-1/2^n).

But in the unlikely event they do lose, their total loss is this sum of losses so far, which we know is 2^(n+1)-2. So we put all of this together in the expectation value formula: the probability of not folding times the gain plus the probability of folding times the loss… and it magically works out to zero. The way to explain this is, when you play this strategy, with very good probability you win make a modest gain, but with small probability you will make a disastrous fall. It averages out to 0 in expectation.

The higher your value of n, the less likely you’ll lose to you when you play. as n approaches infinity, the chance you can fail goes to 0. In this version, where the person can always afford to gamble more, they always make 2. As a lot of you pointed out, the casino also has a maximum bet for this very reason- so everyone has to stop eventually. So this strategy clearly doesn’t work- if you play it lots of times you’ll end up with 0 on average.

But what if you only played a few times? And what if you capped your maximum bet at a very reasonable price- so that you really wouldn’t mind too much if you did lose, even though it does mean you’d lose more often. Let’s try an example. Say you set your maximum times of losing at 4. The probability of that is 1 in 16. So you’d think that you’d be pretty safe if you only played a small number of rounds compared to 16, for example, 4.

You’d lose money unless you won every round. But the probability of that is only around 77%- no were near a guarentee, especially considering how much you stand to lose. Plus the amount you can win is just 8. In my opinion, you’d be way better off getting a job. That solves the paradox entirely for the real world as far as I’m concerned. But there’s still a paradox, in my opinion, mathematically.

Let’s look at the game where the person paying never runs out of money. You might say, well that would require them to have infinite money already. Not really. Each time they play, they only bet a finite amount, and they can always borrow money to play because they’re guaranteed to make it back. You might say, well, there isn’t even an infinite amount of money in the world they could borrow. Sure, but maths doesn’t care about what sort of world we’re in -we could have been in a universe with different physics that allowed the universe to be infinite, and the maths would be the same.

So this is the paradox, mathematically, for me. This random red or black game should have expectation zero. You just feel like that must be true. There’s no way to on average make money from a game of complete chance.

But what’s the expectation of the martingale? Well it’s 2. You always win 2. Or using the mathematical formula, we can see the same thing.

In fact, I can make this number anything I want- for example, say I bet 50 more than my total losses each time- then the expectation is 50. But I can make it worse again, by using this strategy, say you’ve lost a few times so far and it’s the nth round- then bet all that you’ve lost plus 2^n. Look at the expectation value. It’s infinite.

So the real paradox for me is that you can some how take a game that you think should have expectation 0, and then actually make that expectation whatever you want, including infinity, yet when you restrict to only ‘realistic’ cases, you get 0. huh? This paradox showed me that my intuition about expectation values is wrong- there are situations where it breaks down badly. That’s why I really like paradoxes- if the mathematics is sound, it means what’s unsound is something in your own way of reasoning. It forces you to acknowledge that.

I wanted to make this video for two reasons. One: to share my Death Valley experience with friends, family, and you. And two: for it to serve as a guide for those who might be planning their own Death Valley trip- a very loose guide, but a guide nonetheless. Death Valley is one of the hottest places on earth in the summer months temperatures range anywhere from around 100 to 120 degrees Fahrenheit -or more. So as summer approaches, my friend Bobby and I decided to squeeze in a short trip before it gets too hot. I’m at Bobby’s and I think he slept through his alarm, which is funny because the last trip we went on he also slept through his alarm.

I was waiting for you to come out so I could record you and then your neighbor came out the other door and I wasn’t paying attention and I was just recording her. From Los Angeles, Death Valley is about a four-hour drive. It doesn’t actually feel that long though because the landscape constantly changes you’ve got green mountains, red rocks, farmland, small towns, deserts, and that kind of cycles until you get there.

The plan for us was to make it a simple two-day trip: drive out Monday, spend the night in a motel, spend all day Tuesday exploring and then drive home in the late afternoon. I had already researched all the places we wanted to see so fitting it in would just be a matter of timing and managing any random adventures we wanted to take. Our first stop would be father Crowley Vista. Bobby’s choice.

It’s where you can see military jets fly through the canyon. Bobby loves planes. Any time we drive past an airport he wants to stop or at least look so watching jets fly through Death Valley was a must for him. We read online that they fly pretty much every day. Some days you get quite a show and others it’s pretty quiet.

We had no idea what we were going to get. So we found a nice spot on the edge of the canyon and waited and waited and then As ready as we were, it happened so fast. It came out of nowhere. There’s really no warning. As soon as we heard the jet and pointed our cameras at it, it was gone.

At this point we were technically in the park but not down in the valley. That’s where most of the sightseeing is… and the heat. Bobby are you ready to feel uncomfortable for the next 36 hours? oh it’s hot 110. This is also where we ran into our first bit of trouble the air-conditioning in my car started blowing out hot air. Not good.

We still had a day and a half left and ninety percent of it was down here. Death Valley is really just a lot of rocks, sand, and dirt, and heat but it’s also got character and that’s what makes it worth exploring. For example we found this ghost town on the very east side of Death Valley called Rhyolite. It was once a prosperous mining town in the early 1900’s.

Now it’s just abandoned homes, a bank, and a very weird art museum. and then there’s the Mesquite Flat Sand Dunes. Probably one of my favorite stops of the whole trip.

When you come down the mountains and see them in the distance, they look tiny, minuscule, but when you get up close to them they’re pretty massive. And you can just walk out as far as you want. We spent the night in a little town called Beatty. There’s really not much there: a few motels, a couple restaurants, and a Denny’s with the casino attached to it. In the morning we got coffee at a little diner and then headed back into the valley.

Do you think it’s gonna work? I do not think it’s gonna work as well as it should. Does it feel cold? No. Wait, wait, wait. Yes it does.

It feels mediocre. Bobby. No, that’s better. Yeah that’s working. Success.

Day two was starting off strong. Badwater Basin was number one on my places-to-see list. It’s a giant salt flat, nearly 200 square miles.

It’s also the lowest point in North America at 282 feet below sea level. For reference, there’s Bobby and there’s a sign for sea level. Bobby and I just walked out as far as we could.

We’re still walking. The path is getting a little less traveled, a little rockier. Bobby is leading the way. We went early in the morning to avoid the extreme heat, but it was already pretty bad. Bobby heard that the salt here basically tastes like pink Himalayan sea salt so he wants to test that theory out.

No good? That’s the saltiest thing I’ve ever tasted. I I’d put that on some steamed vegetables.

Okay. Alright, so Bobby and I have gone as far as we’re probably going to go. It’s getting a lot hotter, a lot more nothing around here. We’re gonna take a few pictures and then probably head back.

The plan for day two was the started Badwater Basin and then drive back up, hitting all the major stops as we made our way out the park. For the sake of time, I’ll just show you the highlights. Oh and my air conditioning stopped working again after Badwater. Our final stop was Dante’s view. You drive 20 miles up the mountain and you’re greeted with a beautiful view of the entire Valley. It’s cool, it’s relaxing, and as a nice wrap up to the day we could see our entire trip in the valley below.

So it makes sense that I would end the video here, too, right? Well, I can’t. Because that’s not where this trip ended.

As we were leaving, my car stalled out here. We waited a few minute, started to back up again and then it stalled out again here, in the middle of nowhere. I don’t know much more about cars other than how to change a tire, but I do know being stranded in Death Valley is one of the last places you want to be. There’s no cell service, no relief from the sun, and ranger patrol can be few and far between.

There are a lot of details to this story but I want to keep it as short as possible, so here we go: Basically, we were able to stall out again in front of a restaurant that had the worst wifi ever. Here. I was able to get one text message through to my family in Michigan. My dad’s a car guy and would likely know something. He was able to call the restaurant and talk me through some possible scenarios. Since the car was still driveable, Bobby and I were going to make our way out of the park until we had cell service and were near some type of town so we wouldn’t be completely stranded.

And somehow we made it. Just as we were getting off the highway in Lone Pine the car stalled again, the serpentine belt broke, and I was able to pull directly into a Comfort Inn. Side note: this is Mt Whitney.

One of those is Mt Whitney. One of these. It’s the highest point in the contiguous US. It’s kind of cool that we got to see the lowest and highest points in the same day. Anyway, with shops being closed we rented a room, called the tow truck in the morning, and were towed to Ridgecrest 70-something miles away.

Unfortunately the fix wasn’t a simple belt replacement and the total repair cost was 750 dollars. With all that said I did have a good time. It was a rough ending but we did get to see everything we wanted to and we didn’t get stranded in Death Valley. I’ll take that.

Imagine getting the idea one day to sell everything you own, take the money to Las Vegas, and bet it all on a single spin of the roulette wheel. It sounds crazy. The risk of losing is very real, and you could very well be walking away with just the clothes on your back. In fact, the chance of winning in an all-or-nothing red/black bet on an American roulette wheel is 47.3% (48.6% if playing on a European wheel). Ashley Revell of the United Kingdom decided to take that risk when he sold everything he owned and bet the resulting £76,840 (about £105,400 or $164,286 today) on red in Las Vegas during April of 2004. Thirty-two year old Ashley Revell’s journey to risking his life savings in Vegas began, by his own admission, over drinks in a pub with friends.

One friend brought up the idea of betting everything on a single spin of the roulette wheel, and the slightly inebriated group agreed it sounded like a good idea. Despite the conversation being alcohol induced, the next day, the idea still stuck out in his mind. He later told the Telegraph, “I thought what an amazing experience it [betting all of his money] would be. At the time I wasn’t married, I didn’t visit this website. I was completely single.

It was now or never.” It should not be surprising that not everybody supported his plan, and both of his parents opposed the idea. Revell’s father, Mick, told his son that he was a “naught boy”, that he shouldn’t go through with it, and “He should work like all the other kids do.” Ashley spent time convincing them to support him in the endeavor. His father caved first, but his mother took a bit more persuasion before agreeing to support her son.

So he took the next step and began selling all of his possessions and raising a bit of extra cash any way he could. His BMW car, a Rolex watch, golf clubs, and even sentimental items were either sold at auction or during boot (trunk) sales. Some items were harder for him to part with than others, especially soccer trophies and a cricket jumper he received while playing in high school. Afterwards, Revell admitted he regretted selling those items.

Eventually a television crew from the British TV channel Sky One heard about his plan and created a TV mini-series titled Double or Nothing. Tallying it all up, after selling everything and acquiring funds from other sources such as being sponsored to change his name to “Ashley Blue Square Revell” by a UK online bookmaker, he managed to compile a very respectable total of £76,840. With the money in the bank ready to be wired over, he boarded a flight for Las Vegas with the camera crew, his friends, and parents in tow. He didn’t even technically have the clothes on his back at this point as what he was wearing was a tuxedo he rented specifically for the occasion. Plans to place the bet at the Hard Rock Hotel fell through after negotiations broke down with the casino. However, the owners of the Plaza Hotel and Casino seized the opportunity for publicity and agreed to host the roulette game, though directly before he placed his bet told him that they did not advise that anyone, including him, go through with something like this.

Despite the risk, the night before making the life-changing bet, Revell slept well and later said did not doubt his decision to go through with it. Despite the odds technically being slightly against him, he stated, “Thinking back it seems crazy but I was so convinced I was going to win. I was literally going down there to collect my winnings.” However, he still had not decided the answer to an important question: would he bet everything on black or on red? He waited most of the morning for a sign telling him which to choose but none came. In the end, according to Revell, directly after the ball began to spin, “The first thing that came into my head was red, so I just pushed all my chips forward.” With many family and friends there with him watching, along with the audience of Sky One‘s show back home, the ball circled the board before landing on a number- seven, a red color. Revell had doubled his money on one spin, giving him £153,680 (about £210,800 or $328,572 today).

He admitted after the experience that, “… it was a mad thing to do. And I’m thinking back now about what would have happened if I lost. I’d have had nothing to go back to, nothing to wear. But I’d still have my friends, my family, and they’d always be there for me. So they gave me the security to be able to do this.” Unlike most who win big in gambling, Ashley decided that tempting fate once was enough for him.

He declined to bet a second time and cashed in his chips at the table and walked away. As for what happened after, Revell spent a small portion of his winnings on a motorcycle trip around Europe, where he met a girl while in Holland. “I took her back to England with me, we married and now we’ve got two children. You could say I have my bet to thank for finding me a wife. ” One of the many viewers who watched Ashley Revell on the Sky One television program was Simon Cowell.

Cowell was inspired by Revell’s all or nothing bet to create the television game show called Red or Black.

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Thanks for reading! There are plenty more articles on slots rules and tips, the importance of planning your game, and a whole lot of slots vibe. So be sure to check them out, improve your strategies. Remember: when playing, be responsible with your money. I wish you good luck! And don`t forget to have fun!