Lessons in Odds and Probabilities

In the 2008 film 21, six brilliant MIT students become experts at counting cards and use this skill to take several Vegas casinos for millions – until it all goes wrong, of course. But can it really be done?

Yes and no. While 21 is inspired by actual events, the usual Hollywood embellishments apply and you’d pretty much have to be Rainman to pull off anything like that – especially on that scale. However, there are ways in which the average Joe can play a far smarter game of cards – or bingo, for that matter – that takes odds and probabilities into account. Math in casino games is something that can help make a difference to how much you win and playing by numbers is never a bad idea!

How to Calculate Probability

The basic mathematical equation to calculate probabilities is a lot simpler than you might expect:

Probability = 1 / number of possible outcomes

The most basic example we can use to illustrate this is the case of a coin toss. Every time a coin is tossed, there are two possible outcomes – heads or tails. So the probability of the coin landing on either heads or tails is 1 in 2, or 50%.

Now imagine that we exchanged the coin for a three-sided die, but two of the sides are heads and only one is tails. Now the probability becomes 2 in 3 for heads, but only 1 in 3 for tails. In other words, the probability of the die landing on heads is greater than that of it landing on tails.

Odds are Not Probabilities

If you’re at all familiar with horseracing, you’ll know that backing a hundred-to-one shot is the most lucrative kind of bet, but only if your horse wins. This is because casinos and betting houses pay out in inverse proportion to probability. The greater the probability of a win, the smaller the payout. That’s how odds work. In bingo you can look at how many people are playing a game to work out your winning chances. The fewer people, the lower the pot, but the greater the winning chances. It’s all about math!

Probability is Not a Crystal Ball

In theory, you could roll that three-sided die a hundred times and come up on tails every single time, even though the probability for heads is higher. Probability does not predict the future. If you’ve ever played a game involving dice, you’ll know this to be true.

It also doesn’t help to know the outcome of the previous hundred (or thousand!) tosses either. That’s because each event is independent – it is in no way influenced by the last one. Let that be a lesson to anyone who thinks that their odds of winning the lottery increase every time they play, so long as they play the same numbers.

Why It’s Still Worthwhile

After all those warnings, you might be thinking that probability is pretty much useless to you. But that’s not true. By understanding probability and how it differs from odds, you can make smarter decisions when you play bingo. You can weigh your risks more carefully and decide whether you want to take a small risk for a small win or a big risk for a big win.

Plus, a particular benefit of playing online is that you’re free to work out what strategies work for you when you play bingo. You can try a variety of different mathematical applications and see which ones work for you, or you can simply sit back and forget about all the math and play for fun!