## Calculating Luck Probabilities in Mathematical Conundrums, Casino Games and Games of Chance

Luck is an intriguing phenomenon that is never too far away from our lives. Some people just seem extremely lucky. Richard Lustig has won the national lottery seven times with winnings topping £1 million. Lustig claims his winnings are down to strategy, but if the lottery is truly random, how can there be truth to Lustig’s claims?

If Lustig decided to play online casino games would he be able to apply a strategy to beat the online casinos? There are lots of gambling strategies which, on the base of things should not play a part in beating casinos, but due to complex mathematical probabilities it means they do play a part.

We have outlined several proposed strategy methods below which claim to go beyond luck and coincidence. We would not recommend utilising any of them, but they will change your perception on exactly what constitutes luck opposed to randomness.

One small but discreet change in odds can have a significant impact on the outcome of any game involving luck and probability.

#### The Monty Hall Problem

In the last quarter of the 20th century, there was a column written in Parade magazine by Marilyn vos Savant. Savant held the record for the highest recorded IQ and in her column, she would solve mathematical puzzles which were sent in by the readers of Parade magazine. One day, Savant was posed a question by one reader which was based on the ‘Let’s Make a Deal’ gameshow whose host was called Monty Hall – hence the name of the conundrum.

The scenario in the Monty Hall problem is thus: A game show contestant is shown three doors. Behind one door is a prize car but behind the other two are prize goats. The contestant knows this and must pick one door in the hope that they pick the door with the car behind it. Let’s imagine that the contestant picks ‘Door 3’. They still do not know what is behind their chosen door but now the host will open a different door to the one the contestant has picked. The host cannot open the same door as the contestant nor can the host open the door which is hiding the prize car. Monty Hall proceeds to open a door to reveal a goat, let’s say it is ‘Door 2’. With Door 2 opened and one goat revealed, Monty Hall now gives the contestant the choice whether to change their choice of door to Door 1 or sticking with their original choice of Door 3.

Savant is asked whether changing the initial choice of door now that one has been revealed would increase the probability of revealing the door with the car behind it. One would think at first that it would not make a difference. One door contains a goat and the other a car – this is a 50/50 decision regardless, right? Savant states that the contestant should always switch doors to be in with the best chance of winning the cars, but why? For starters, Savant’s reasoning has been proven to be 100% mathematically sound. The table below showcases why the contestant increases their percentage odds of picking the Door which contains the car behind it by not sticking with their original choice of door.

Behind Door 1 Behind Door 2 Behind Door 3 Result when sticking with Door 3 Result if switching to remaining door
Goat Goat Car Wins car Wins goat
Goat Car Goat Wins goat Wins car
Car Goat Goat Wins goat Wins car

The contestant has a 2/3 chance of winning the car if they switch from their original choice of door, but only a 1/3 chance if they stick with their original decision.

Changing doors really does make a difference to your chances of winning the car in this case. Many mathematicians refused to believe the change in odds until they were shown a computer simulation. By making one decision, the contestant is able to double their chance of winning.

#### Odds of Winning Playing Megaways Casino Games

Megaways is a type of online slot which utilises a mechanic that changes the number of paylines on an online slot machine. The mechanic allows for potentially unlimited ways in which to hit a win. The Megaways mechanic was invented a few years ago by Australian online slots development company, Big Time Gaming.

According to Megaways Casino, Megaways slots work on a six-reel structure with an added addition of an extra horizontal reel with four symbols. The addition ensures that each spin can give players the opportunity to hit two to seven symbols per reel. This increases the number of ways to win even though the addition of an extra horizontal reel seems incredibly minor.

The mechanic uses a Random Reel Modifier to change the number of rows on each reel after every spin. Whilst standard video slot games have a fixed number of paylines, the Megaways engine ensures that each and every spin is unique and unpredictable. In fact, the mechanic allows for up to and over 500,000 different outcomes.

By playing online slot titles which utilise the Megaways game engine, players can increase their chances of winning greatly.

#### Lottery Tips from Richard Lustig

An American who came to prominence following his multiple lottery wins, Richard Lustig claimed he had a winning lottery strategy. Of course, following his wild claim, everyone wanted in on the winning strategy too. Lustig released a book with the title ‘Learn How to increase Your Chances of Winning the Lottery.’ With a title like that it did not take long for the books to go flying off of the shelves. Lustig states that gamblers can increase their chances of winning the lottery based on how you pick your numbers and how you spend your lottery winnings.

Firstly, Lustig states that players should always choose their own numbers. However, this has come under some criticism. Statistically, it has been proven that around 70% of all lottery wins come from Quick Pick tickets. These are the tickets where the numbers are picked by a machine at random. On the other hand, many have argued that the Quick Pick option is a lot more common than the option of choosing one’s own numbers.

However, there are other doubters to Lustig’s tips. For one, the most picked lottery numbers are below 32 as people tend to pick numbers which have a significant meaning to them. This means that many players could end up splitting the prize with other likeminded people who pick the exact same numbers. Quick Picks, on the other hand are random and will often include higher numbers. Lustig’s other tip is to reinvest your winnings into more lottery tickets. From a probability point of view this is a sound strategy as statistically, the more tickets you have the greater chances of winning you have. However, even this is a little illogical, as if you are constantly reinvesting your winnings, then what is the point in playing in the first place?

#### Final Words on Probability

When it comes to games of chance and casino games, there will always be a percentage sum which will determine how likely or unlikely a player is to win. The first step to winning on any casino slot or game of chance is to try to calculate how likely you are to win or not. When it comes to online slots, this is easy as, more often than not, the casino will tell you the exact RTP (Return to Player) odds of any slot machines. However, games of chance such as the lottery are a little harder to calculate. Of course, the easiest way you can give yourself a greater possibility of winning the lottery is by simply purchasing more tickets, but this is not something we would recommend.

Overall, the knowledge stated in this article is almost impossible to apply in any practical sense. Casinos, bingo halls, lotteries and all other similar games all go to huge lengths to ensure that games remain fair and chance based. The proprietors of all of these games go to extreme precautions to ensure fairness at all times. With that being said, there are ways to beat the system. Online sports bettors took advantage of human error and a loophole (or in this case slowness) to win thousands of pounds from bookmakers on tennis betting for example.

With continued advancement in technology, however, it seems more likely that ‘beating the system’ will get much harder as computers and robots take are programmed to spot even the tiniest details.