With the release of free trade, there has been new emergent game play - gambling! Go to any busy world, and south of the Grand Exchange you'll see a hundred or more players screaming over each other, "Dice Game, 60+ 2x!!!" The premise of this game is simple. You join their clan chat, trust them with your bet, and hope the dice roll 60 or higher. At first it seems simple, easy to play, and easy to win. Unfortunately, its not that simple. There are many more variations on this dice game, so lets take a look at their expected long run earnings, and a look at gambling in RuneScape in general.
If you've ever taken a course in statistics, you'll know that probability is a way of expressing knowledge or belief that an event will occur or has occurred. There are two ways to interpret probability: as a frequentist, "in the long run," or as a Bayesian "a degree of rational belief given the evidence." If you're confused, don't worry. That's about as deep into statistics as I'll go and I'm only going to stick with the former.
Most veterans of RuneScape or those familiar with economics will understand the concept "in the long run". What does it mean to be "in the long run"? It means to perform an experiment over and over, more than you'd ever want to know. In the long run means the house, the casino, the player hosting the dice game, are the ones making hundreds to thousands to millions of bets. As the prospective better, rarely should you be able to consider yourself to be "in the long run." This is why placing one or two bets may be very profitable, but only if its one or two.
As a statistician, you can calculate the range of expected values for a small number of bets using something called a confidence interval. If you're interested, I'd suggest you'd search for "confidence interval" or "binomial random variable", as the bet you'll be making usually have two outcomes (win, or lose). This is beyond the range of the article, so I'd like to refocus on "in the long run."
The probability that a standard, fair six sided die will roll a given number is 1/6. The probability that one of Jagex's percentile dice will roll a given number, 1-100, is 1/100. This is important to keep in mind when calculated expected payouts. We'll see that calculating expected payouts, in the long run, is as simple as doing a bit of counting, and multiplication.
Lets start with the most common game - 60+ 2x. The probability that percentile dice will roll from 60 to 100 is the probability that the percentile dice will roll 60, plus the probability of 61, plus 62, ... plus 99, plus 100. That is to say, 1/100 + 1/100 + 1/100 + ... + 1/100 + 1/100. From math class, remember that you can factor out the 1/100, and get 1/100 * (1 + 1 + 1 ... + 1 + 1). The (1 + 1 + 1 ... + 1 + 1) is the same as (100 - 60 + 1), so the probability of rolling 60 to 100 is 41/100. Multiply this number by the payout, which is two times the bet, to get 82 / 100. Since for every bet made you have to pay the house, subtract out 100 / 100. The final result is -18/100, or -18%. That means that for every bet made, the host is expected to take 18% of it.
There are variations on this common game, such as 60-84 2x, 85-99 3x, 100 4x. In the interest of space, the expected payout is 1/100 * ( 84 - 60 + 1) * 2 + 1/100 * (99 - 85 + 1) * 3 + 1/100 (100-100+1) * 4 - 100/100 = -1/100 = -1%. This is still a losing prospect for a gambler in the long run.
The house always wins.
If I haven't convinced you to avoid betting with the long term prospects, here are some tips to spot a legitimate player:
1. They'll show their wealth if you ask them to. Quite frankly, they'll demonstrate they'll be able to honor their maximum bet. Some players will do this by wearing their wealth. Be warned, though, a rare can be lent, GP can't.
2. They will refuse bets they cannot honor. Think about it, someone out to scam you will be gleeful that you place a 10m bet. More money for them to log with.
3. Unknown players will allow you to bet a small amount. If the player refuses a bet in the range of 1k - 50k, they're probably looking to scam you.
4. They have been doing this for a long time. In order to place a bet with a legitimate player, they'll require you to join their clan chat to see the result of the dice. You can join a clan chat in advance and watch other people place their bets.
5. The old rule of thumb: if it seems too good to be true, it probably is. Legitimate players will never knowingly offer you an edge.
6. They announce how much people are betting, and what they're betting. They will announce the result of the dice roll, and if players win. They will always allow for more bets.
7. Their payouts will not be different than their bets. GP for GP, items for equivalent items, never items as a reward for GP bets, especially if the item value is far above the asked GP bet.
Gambling in RuneScape really has two parts. The first is a gamble on a trust trade, the second is a gamble on the result. In the long run, even after finding a trustworthy player to bet with, gamblers will still lose. I've watched player after player put up millions of GP, all because they don't understand probability and statistics. If your eyes glazed over when skimming through all of this, please understand this one important point: The house always wins.