Odds are what dice games are all about. The skill in a dice game is working out when the odds are in your favour and they don't have to be a huge percentage in your favour to work for you.
Odds are the ratio between the number of winning possibilities and the total number of all remaining possibilities. So the chance of throwing any single number with a six-sided die is 5 to 1. If you bet on a single number being thrown and were paid out at 4 to 1 (not 5 to 1) you can see that you would be at a disadvantage. IWhen you playt games like online bingo for money this disadvantage is known as the House Edge.
Casinos make vast profits with an edge as small as 0.7%. If you've looked at the hustlers', operators' and casino dice games you will have an idea of how lucrative odds can be. Craps offers the best odds in a casino if you know what your're doing but you can be sure that any dice game a casino, operator or hustler offers, has the odds in their favour.
If we assume that we have an honest game with straight dice and that every roll is random then the odds can be assessed.
There are six possible outcomes with a throw of a single standard die. For every extra die thrown the number of outcomes is multiplied by another six. So, with two dice, the number of outcomes is 36, and with three dice you multiply by another six to get 216 outcomes. To work out the odds of a certain total being rolled work out how many combinations of the dice make it, and subtract that number from the total number of outcomes possible. This number and the number of combinations that make the desired total, give the odds.
For example their are six ways to make a 7 with two dice (1-6, 2-5, 3-4, 4-3, 5-2, 6-1) and 36 (6 x 6) possible outcomes, so the odds are 30 (36 - 6) to 6, or 5 to 1. Note that 2 - 5 is not the same combination as 5 - 2. The numbers are on different dice. A series of dice all showing the same value can only be made as one combination.
What follows will dispel a few myths about gambling odds and hopefully you will learn how to tell the difference between a wise bet and a foolish one. Pigeons, mugs and suckers are easily parted from their money. A player is someone who knows the odds and makes decisions based on facts and the true odds.
The odds of a specified outcome are always the same on every throw of the dice. You could roll double-6 ten times in a row and the chances of the next roll being a double-6 will still be the same - 35 to 1. The odds for any outcome are the same for every roll. It is a common misconception by gamblers that this is not true. Odds work out over a period of time and over a number of random results. A casino that takes thousands of bets an hour knows this. The law of averages works over the long term. If you throw a die an infinite number of times the results will match the true odds but the lower the number of rolls the more the results can differ and a gambler can lose a lot of money waiting for the law of averages to work for them, with no chance of recouping it.
Similarly the guessers disadvantage is a gamblers theory that a player who makes bets on instinct or feeling with no set pattern will do worse than someone who bets in a disciplined methodical way. A 50-50 chance will always be a 50-50 chance every time and a random bettor will have the same odds of winning as someone who consistently bets on the same outcome.
Having said that the chances for any specified outcome are the same for every roll, the chances of rolling a specified outcome within a specified number of rolls is more complicated.
The Sixes and Double Sixes Bet illustrates an interesting point about odds. The story goes that a French gambler called Antoine Gambaud the Chevaliere de Mere, was making a good living from the Sixes Bet. The bet was that he would roll a 6 within 4 rolls of a die. With 6 possible outcomes of a throw of a single die we can see that an even money game should have been three rolls and that he had a good edge. But after time players refused to play him and so he came up with the Double Sixes Bet. That is that he would roll a double-6 within 24 rolls of the dice. He worked out his game, without modern maths, by multiplying the 4 rolls he originally used by the number of combinations of the second die (6) to get 24 throws. You would have thought that the number of rolls should have been something greater than 18 since there are 36 possible outcomes of two dice and only one double-6 combination. However he soon found that he was losing money and so he approached the French mathematician and scientist Blaise Pascal (1622 - 1663) with the problem.
It was Blaise Pascal with Pierre de Fermat who came up with the basics of probability theory. Pascal concluded that the true odds were the odds against winning in one roll multiplied by the colog of the hyperbolic log of two (0.693). This works out as 35 x 0.693 which equals 24.255 rolls for an even money game. He needed at least 25 rolls of the dice to get an edge and 26 or 27 would have been more like it. The story goes that he took this advice and soon recouped his losses.
Even today many gamblers still calculate the odds the way I would have. 36 combinations and 1 way to make a double-6 would give even odds at 18 rolls. The story goes that in the USA during the 1950s a gambling operator called Fat the Butch was so convinced that this was so, he bet $1,000 a time on Double Sixes and was allowed 21 rolls of the dice, in each game, to achieve it. He gave up 12 hours later having lost $49,000.
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