The Math Behind The Game • Autobetic

The Math Behind The Game • Autobetic

Like Craps, the Sic Bo table can also seem intimidating if you’re new to the game or a casino environment. It’s probably not a table that fresh players will head towards the first time they enter a casino.

Way Beyond Asia Now

But, relax — because it’s a really easy game to play. So simple, in fact, that you can learn it in just 2 minutes through this YouTube video. Some time back, this game was predominantly found in Asian casinos; nowadays, you’ll see it just about everywhere. And for good reason: it makes the casinos great money while offering players the illusion of a favourable bet.

This illusion is a rather clever one. It’s like one of those sneaky little things you don’t notice until somebody points it out.


You're welcome

Darn! Why didn’t I see that?


Most Bewildering Bet

Sic Bo literally translates to ‘Precious Dice’, and also commonly goes by the name ‘Big Small’. There are many bets you can choose to make at the table, as you would have seen in the video. And if you’ve been religiously reading this blog, you should by now be able to calculate the odds and EV of those bets. However, the most confusing one happens to be the most basic bet of wagering on a single number.

Initially, it seems like a fair bet to most people. That’s because 3 dice are being rolled, and you can bet on any of the 6 numbers. If any of those 6 numbers appears on any of the 3 dice, you get paid 2:1. Logically speaking, you thus appear to have a 50:50 chance of hitting one number (3 dice versus 6 choices) and you get paid 100:50 (2:1). So it’s all good, right? Nope — wrong.

Here’s The Math On Sic Bo Odds

If we were using just 1 dice, your odds of picking the right number would be 1 in 6. That means you’ll probably get it wrong 5 out of 6 times. Using that same logic with 3 dice, the odds of your number not appearing on any of them would be:

(5/6) x (5/6) x (5/6) = 125/216 = 0.5787 = almost 58%.
That’s much lower than the 50:50 odds you had assumed earlier, isn’t it? You’re going to get it wrong 58% of the time, mate!

Let’s work out the rest of your odds:

Chances of hitting 1 number = (1/6) x (5/6) x (5/6) = 75/216 = 0.347 = 34.7%.
Chances of hitting 2 numbers = (1/6) x (1/6) x (5/6) = 15/216 = 0.0694 = 6.9%.
Chances of hitting all 3 numbers = (1/6) x (1/6) x (1/6) = 1/216 = 0.0046 = 0.46%.

And the overall Expected Value of Sic Bo turns out to be:
[(75/216)(1) + (15/216)(2) + (1/216)(3) + (125/216)(-1)] = -0.08.

Smallest Bang For Your Buck

If you’ve read my two other articles in the Casino Math Odds series on Roulette and Craps, you’ll realise that Sic Bo gives you the lowest value of all three games. And it does this while cleverly hiding behind the facade of ‘fair play’. Sneaky, isn’t it? Well, at least now you know. Good luck!


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Images: mammaoca2008, Max Sat


Author: Joseph Johnson