Gambler’s Fallacy or Gambler’s Opportunity

The Casino de Monte-Carlo is one of the world’s most famous casinos. It’s also one of the oldest. It originally opened in 1863, 156 years ago. It was the epitome of all things ‘Monte-Carlo’.

If you’ve ever been, it’s perched up high on the hill by ‘Casino Square’. It has views out over the Mediterranean and the harbour with the billions worth of mega-yachts. If you still can’t spot it, you can always look for the array of supercars parked out front — Lamborghinis, Ferraris, Bugattis, the place just reeks of wealth.

Personally I’ve been there twice. Never to play, just on day trips as I’d been travelling through Monaco. The first time, in my early 20s, I sat by the bars in Casino Square. After nearly choking at the cost of two beers, I decided to spend the next two hours in the cinema watching Cleaner while I waited for a train over to Genoa and then on to Florence.

The second time, thankfully, I was prepared for the cost. After lunch by the harbour and several beers later by Casino Square, a drunken train back to Nice was a little more fun.

Still, it’s a crazy place with seemingly endless amounts of money floating around. And the casino must see some pretty high net worth whales come through. The casino is so famous it was even the setting for Never Say Never AgainGoldenEye and the Ocean’s film series.

It’s easy to burn through cash in Monte-Carlo and we’d think that if you were at the tables in the Casino, you’d burn through a whole lot more.

But it was on 18 August, 1913 that serious money was washed from the hands of speculative gamblers.

The gambler’s fallacy

Roulette is a fairly simple game to play at a casino. There is a flat spinning wheel which has a small white ball sent flying around with the aim to land on any given number. Most roulette wheels will have numbers from either double zero (00) to 36 or from single zero (0) to 36. Occasionally you might see a triple zero (000) table, but it’s nowhere near as common.

The idea is you place bets either on numbers or combinations of numbers to win. The numbers are all colour coded either black or red (and green for the zeros), so you can also bet on the colours.

Typically the single numbers will return 36-to-1 in terms of odds. So let’s say you put $1 down on 11 and the little white ball landed on 11, the table boss would return you $36 (including your original bet). The fact there are 37 numbers (including the zero) gives the house the edge.

But as you can imagine, landing on any single number out of 37 is pretty statistically unlikely. That’s why you often see more bets falling on splits of numbers or, in particular, on the red or black bet options.

You see, red or black is a simple 2-to-1 odds outcome. You bet on black and black comes up, you double your money. $1 down would come back as $2. Simple.

What you need to understand before I go any further is something we call the ‘gambler’s fallacy’. The idea is that if one outcome occurs more frequently than another, the likelihood of the other one occurring next becomes more likely.

This is a fallacy on a game like roulette, because with every spin of the wheel, the odds of any particular outcome resets and is exactly the same.

But human psychology and the idea of winning ‘streaks’ stops many people at the tables from realising this truth, hence they succumb to the ‘gambler’s fallacy’.

Now sometimes you’ll see people trying to use the gambler’s fallacy to their advantage. The gambler’s fallacy system works like this…

You place a $1 bet on red, and you lose, the outcome is black. Therefore the next bet you place is $2 again on red, that way if red comes up, you win $4, getting back your original $1 you lost already and what you would have won the first time but didn’t, plus your current money.

In short, this second bet recoups your losses and brings you back to square one. And because black already came up, the chances of red coming up next must be better — remember, every spin the odds are the same…

But then your second bet of $2 also loses and the result is black. Damn. Well, that’s two blacks in a row, red must be comingsoon. So you bet on red again, this time with $4. And if red comes up you’ll get back $8. That covers the $3 you’ve already lost, plus your current bet.

Except you lose again and black comes up again. That’s three blacks in a row. Well, that must mean that red is statistically even more likely to come up next time! At this point, the gambler is well and truly entrenched in the fallacy, and it’s very hard to get out.

So they next place $16 down on red. Again the idea is that with so many consecutive black outcomes, red must be more likely to come up next…except it’s not. But this $16 would recoup all the existing losses and return the gambler back to square one.

Except you lose again. Oh dear.

This process of doubling down and doubling down psychologically has merit — but statistically none. And when you do the maths, just 10 consecutive black outcomes (in this example) would mean the gambler is down $1,023. After 20 consecutive black outcomes (in this example) they would be down a whopping $1,048,575, just from a starting point of $1.

Now most people don’t have this kind of bankroll, so just a few adverse outcomes against the player and most would get wiped out.

And the fallacy still has people believing that the statistical outcome of that many consecutive outcomes going against them is near on impossible. It’s not. Every spin, the odds of every outcome are exactly the same — this is the fallacy working at its finest.

And if you thought 20 outcomes against the gambler was big, how does 26 sound?

The Monte-Carlo fallacy

Now this ‘gambler’s fallacy’ is also known as the ‘Monte-Carlo fallacy’. The reason for this is that on 18 August 1913 there were 26 consecutive black outcomes.

Of course, after the first few, the fallacy kicked into full swing. And people began flocking to the table to bet on red as the next outcome. The longer the streak of black went on, the more money that went down on red, certain the next one would come good.

But 26 times it did not. Now if you’d been trying to apply the system to beat the fallacy, you’d need to have a bankroll of $134,217,726 just to break back to even. That would mean $67,108,863 in bets lost, and then the same amount (plus $1) to make the 27th, and finally winning the bet that came up red.

Needless to say on that night, the Monte-Carlo casino had an exceptional night for the house.

And since 18 August 1913, the fallacy has been predominately known as the Monte-Carlo fallacy.

To try this system today to beat the fallacy is really idiotic. And you should expect to lose. There’s simply no way that any sane person — even with that kind of bankroll — would apply it.

The fallacy statistically remains true and will always remain true in perfectly balanced games of chance, with 2-to-1 outcomes.

But even with random chance and statistical outcomes resetting with each roll, the fact is there is always a chance your outcome will come up.

And that chance is what makes gambling so appealing to some.

So it makes sense that any new currency that develops is going to find some way to exploit this double down psychology. And that includes cryptocurrency.

There is a game in the crypto world that is effectively a crypto chance game. You bet crypto and get to bet high or low. You can set your own odds effectively, but in the 2-to-1 outcome the result is either a number lower than 49.5 or higher than 50.5 (up to 100). You choose higher or lower. The house edge is the numbers in-between those two.

With crypto, you can bet the equivalent of 0.00001 of a cent (in the particular crypto of course) and choose higher. The number could come up as 51.8 and you’d win back 0.00002.

But if the outcome goes against you, then you could apply the fallacy system and try to double down and down and down. Based on that you could get to the 27th game and only need a total bankroll of $1,342.18. Still a heck of a lot of money to gamble, should you ever get to 27 consecutive outcomes against you, mind you…

Now, we’re not advocating you go out and start trying this system and gambling away money or crypto for that matter. Casino gambling isn’t something we’re a big fan of. But it’s interesting that such a risky activity is still being played out in this new wave of cryptocurrency.

Regards,

Sam Volkering


Sam Volkering is one of the editors at Money Morning New Zealand, and is its small-cap, cryptocurrency and technology expert. He’s not interested in boring blue-chip stocks. He’s after explosive investments; companies whose shares trade for cents on the dollar, cryptocurrencies that he believes could deliver life-changing returns. He looks for the ‘edge of the bell curve’ opportunities that are often shunned by those in the financial services industry. Sam specialises in finding new, cutting edge tech and translating that research into how the future will look — and where the opportunities lie. It’s his job to trawl the world to find, analyse, research and recommend investments in the world’s most revolutionary companies.


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