The brutal maths in the ANZAC Day game of two-up everyone should understand

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Bars around Australia today will be filled with raucous crowds enjoying the coin-tossing game of two-up.

The most important thing to remember about the mathematics of two up is that the chances of a heads or a tails being the result in one throw are the same every single time.

As economic commentator and topical wagering enthusiast Stephen Koukoulas pointed out this morning, the odds of “heads” or “tails” is always the same:

This can be a little bit confusing if you get paranoid about a “run”, or a series of throws that result in the same outcome, and especially if you’re onto your fourth beer. Here’s how you calculate the chances of throwing “heads” four times in a row:

So this shows simply that the chances of this happening are one in sixteen. But note that the chance on any throw – I’ve highlighted the fourth below – is exactly the same as the others:

So when there is a run of either heads or tails, while it makes mathematical sense that the next throw will come up with a different result, remember that the odds remain one in two.

How to avoid losing your money

There’s no way to “win” at two-up but there is one approach to ensure you don’t lose your money. You need to be prepared to keep doubling down on your bets, however, and that could clean you out if you’ve got a limit.

If you lose $5 in the first round, double your bet in the next round to $10. If you lose that, double your bet again to $20, and so on, until you win back everything (risky, of course, when you need to pair up with someone who also wants to meet your bet of $80 or more.) But when you are square, return again to your $5 bet and if you win, only bet $5 again.

The mathematics can get more complicated when you factor in “odds” – a toss of one head and one tail five times in a row. But if you’re just enjoying the game, remember the odds are one in two on every throw.

Come in spinner. Enjoy the day.

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