In some casinos, you’ll see a “Big 6 and 8″ at the corner of the table and a large area to make “field” bets. The “hardways” and “one-roll” bets virtually shout out to you with their dice diagrams. Forget all of them. They’re like adverts for bad bets, and the Casino Games would love you to make those bets on every roll.

The best bet on the dice table isn’t even printed on the table. The best bet on the table is the “free odds” that you get to place behind your pass-line bet. Pass-line bets are paid at even money. If you bet £5 on a shooter and he rolls a six as the point, and makes that six, the dealer will pay you £5 for your pass-line bet. The house has a small advantage of 1.4 per cent on pass-line bets.

You can reduce that advantage substantially by putting up free odds, an additional bet that gets paid at the true odds of the number rolled. Let’s say you bet £5 on the pass line, and the shooter rolls a four. The odds of rolling a four are 2-1, but you only get even money on the pass line. But if you take free odds, you get paid 2-1 for your free odds because there are only three ways to make a four, while there are six ways to make a seven.

The ten and four are called “sister” numbers because the true odds of rolling a four and ten are the same. Other sister numbers are the six and eight, and the five and nine. The free odds are more complicated for these numbers.

When you roll a six, there are five ways to make a six, while we’ve seen there are six ways to make a seven. So if you have a £5 bet on the pass line, and back that up with £5 in free odds, and a six is rolled, you’ll get paid £5 on the pass line, and £6 on your free odds, for a total payout of £11. The same is true for the eight.

Now the five and nine are a little more complicated. There are four ways to make the five or the nine. So true odds are 6-4, or 3-2, or 9-6.