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What are the odds? How to stop the casinos taking your money

Given the recent legislation changes in the USA, I think it only prudent to start this article with my own views (if you don’t agree with them, you’re welcome to stop reading!). Gambling in itself is not immoral. So long as the gambler is in control and is only spending ‘leisure’ money, it is no more immoral than fishing or any other hobby. Only when it becomes an uncontrollable addiction does it become so; when the gambler is spending money earmarked for some more worthwhile expense.

Accepting the above, this article is designed to help you spend your leisure gambling money a little more wisely and, hopefully, give you more enjoyment from your chosen pastime.

So, let me state right from the outset the Golden Rule of gambling:


So why does anyone gamble? Because the opposite is also true:


In the long term all events tend towards their probabilities. (For those unfamiliar with odds and probabilities, read the ‘What are the Odds’ section below) In other words, given enough spins of a single-zero roulette wheel, all the numbers will come out, on average, 2.777% (1/36) of the time.

In the short term, this doesn't happen. Given 36 spins, 36 different numbers will almost never come out. There is always a discrepancy between predicted probabilities and actual events.

Unfortunately, there's no way of knowing (no matter what systems people may say) which events will come out ahead of probability and which behind, but it does give us the basis for a betting strategy which, if applied properly, can ensure you lose small and, hopefully, win big.

The House Edge

The house edge is an indication of how much a casino expects to win on any particular game in the long run. It is calculated as the ratio of the average loss to the bet. For example, the house edge in blackjack is 0.6%, so we can calculate that the casino expects that for every £10 bet it will make a profit of 6 pence.

In the short term, however, the casino's profits can be much higher or lower, as can its losses.

The house edges for 4 example games of chance (and variations) are as follows:

Pai Gow Poker : 1.46%
Sic Bo: 2.78 - 33.33%
Keno: 25 - 29%
Punto Banco: 1.06 - 14.36%

Getting the edge

Getting the edge is essentially about knowing the expected odds and comparing them to the observed results in any one session on any game.

It comes down to what kind of gambler you are. For example, would you bet on a horse at 10/11, expecting to win, or on a long shot of 25-1, hoping to win? In each of the game edge pages, we'll point out the bets to target based on your gambling style.

Betting strategy

Putting this information together, we can devise a betting strategy which can, at worst, help to minimise losses and, at best, help us to find those big wins.

The first thing to understand is that we're looking at a strategy over a number of sessions, large enough to offset freak results, but not big enough so that the long term odds start to apply. This means that some of your sessions will be losing sessions, but some will be winners. Don't expect to win every time - know your session limits.

Let's say we start a session with a bankroll of £100 and are making £2 bets on a 50-1 chance (0.02 probability, 2% chance.) According to long term probability, we should end up equal, but 50 bets is not long term, so that doesn't apply.

The key to understanding this is to say that if a 50-1 chance comes up on the first event, the chances of it happening again are still 50-1, so don't wait for the other 49 events, get out quick!

Don't give the probabilities the time they need to apply.

If it happens on the 50th event, you'll break even. If it happens on the 51st, you'll lose.

If you always bet until the bankroll is gone, you will be a loser overall. The key to this strategy is keeping all sessions (losing and winning) short.

There's no way to escape the golden rule and, if you play long enough, the probabilities will kick in and bite you, but if you keep your losses down and don't gamble away your winnings, in the short term you could come out ahead.

To summarise:

Stop after a win (quit while you're ahead!)
Change games/casinos frequently, especially when you're on top.
Set a limit to your losing sessions ie a number of bets, not an amount of cash.
Don't bet good money after bad ie when you've lost, quit.

The Edge

No gambling system is guaranteed to win - if it was, the casinos would be out of business. But clearly some people do win at casinos, both real and online. We can guarantee that those winners have followed a policy very similar to the one given above.

Know your game; know your limits - and good luck!

What are the odds?

Before you can get 'the edge' it's important that you understand how odds are calculated.

Odds can be expressed in a number of ways:

PERCENTAGE eg 97% (97% chance of the event happening, 3% of it not)
PROBABILITY eg 0.7 (0 = will never happen, 1 = will always happen)
FRACTION eg 1/6 (1 chance in 6 that it will happen)
RACING ODDS eg 9-1 (9 chances against 1 ie 1/10)

To understand your chances of winning any bet, you must know the odds.

For any action, the sum of all probabilities is always 1. Some events are much more likely to occur than others, but any event CAN happen.

For example, it's possible that a fair coin tossed 4 times will always come down 'Heads'. The odds for this are 1/2 x 1/2 x 1/2 x 1/2 = 1/16 (or 0.0625 or 6.25% or 15-1). Obviously, the odds for it NOT happening are 15/16 (or 0.9375 or 93.75% or 1-15)

At this point, it seems prudent to point out the 'Gambler's Fallacy'. Before a coin is thrown, the odds against throwing 4 Heads were 1/16. The odds of 3 Heads were 1/8. However, after 3 throws, the odds of Heads coming up again are the same as they ever were ie 1/2, as 1/8 x 1/2 = 1/16.

This is an important rule for gamblers: Just because an event hasn't happened for a while doesn't make it more likely to happen.

As stated above, in the long term the casinos always win. They know the probabilities and these are reflected in their payouts - likely events pay small, unlikely events pay big.

Before you begin to gamble, you have to know what kind of gambler you are. Are you looking for lots of small wins, or do you want that one massive win?

Understanding the odds of these events happening should help you calculate your chances.


The above article was written for and remains their copyright

About the Author: Andy Follin is an amateur statistician with a life-long ambition of ‘beating the odds’. He also enthusiastically promotes sites such as which help leisure gamblers beat the odds.

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