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Editorials: Minigames and Sidequests: A throw of the dice

This editorial does not necessarily represent the opinions or attitudes of the Suikosource staff. Any claims being made within are solely the responsibility of the original author. The following work is copyrighted to its original author.
Editorials: Minigames and Sidequests: A throw of the dice by Shirofan

A throw of the dice

Many people automatically assume that Chinchororin is a gambling game played in Japan using the same rules as those found in the first two Suikoden games; this is extremely unlikely to be the case, but that does not mean that the game as performed in Suikoden has no relevance to oriental gambling.

Dice Games and gambling

Dice games are popular throughout the world for their use in gambling pursuits and there are many games played in the South East Asia region. While western games such as craps tended to restrict the number of dice and create baffling rules about which rolls are required; the oriental method was to increase the number of dice but keep the possible results obvious. Both systems are effective in their own way to prevent the common player from discerning the odds of how successful they can be at the game, and thus disguise how much the odds are stacked in favour of the house.

Two dice games do exist but they are rare; most games are three or more, up to about eight dice tossed in a single roll. But the more dice there are the simpler the game's possible scoring outcomes become.

While the exact playing details of the games themselves vary from region to region, country to country, several common factors tend to recur: foremost of which being that several throws have greater significance than others, and corresponding consequences financially. For three dice games these are the ones people are familiar with in Chinchororin: namely the triples and the 1-2-3 and 4-5-6 combinations.

In games featuring just the player and the house then the player is in general given one attempt to make a scoring throw, namely a double, triple, 1-2-3 or 4-5-6 combination. The triple and 1-2-3/4-5-6 combinations generally result in multiplying the stake to the player or the house. In such cases a double and a 1 is generally classed as a losing throw to give more bias to the house; in some countries where the tradition is to colour both the 1 and the 4 red then a triple 4 or a double and a 4 can have the same consequences as receiving a corresponding result with a 1.

Games featuring a group of players with no obvious house tend to have the player roll until a scoring result is obtained. In the event of a significant result the player may have to pay, or be paid by, the whole group playing. In the case of a double, it may be that double and a 1 (and possibly 4) is treated as a significant result, then the player is competing directly against his neighbour, who has to get a better result than the first player. In some cases the difference in result can have a bearing on the amount paid to the winning side.

The closest game to Chinchororin is Japanese in origin, the above variant is Chinese, and this makes use of the three rounds system to get a scoring roll. In this instance the game requires several competitors and does not feature a house. Instead one player has control of the dice for the round and continues in control having better scoring chances until beaten by one of the opponents; much like the position of dealer in various card games. Then the next person in line takes over as the house and so on until the game stops.

As noted above the worst results tend to revolve around the 1, and the best around the 6,so loaded dice were commonplace; it was a skill comparable to card sharps on substituting them at the right moment. Other techniques would have been employed to draw people to the game, such as an accomplice who wins more than he should, or a demonstration by the house that the dice were not loaded in any way would be undertaken before the dice would be skilfully substituted.

So why is Chinchororin unrealistic?

From the above it appears as though Chinchororin sounds like a reasonable merging of the group and house style games, so why was this essay started saying that under the rules seen in the Suikoden games then Chinchororin is not likely to be just another variant on an oriental dice game?

The main reason why not would be that the house always throws first: some people may be gullible, but even they are unlikely to play a game where you may have to pay triple your stake without ever picking up a single die. Regardless of the statistics of the situation the idea of any gambling establishment is to convince the prospective player they can win big and alleviate suspicion that the game is rigged; as such if the house plays then the player would be expected to throw first.

Secondly the three throws per person to get a result seems to be an odd way of doing things for a house based gambling game as most versions of similar games do try and avoid draws whenever possible. Since no score is not an instant loss it would be expected that the player carried on until the dice yielded something in the scoring bracket, or that each player would get one throw to make a score so that the game would be fast paced. Three seems to be a compromise, albeit a historiclly accurate one, solely for the purpose of making it work in a videogame context so that it can keep the game from taking too long, and the oddly biased rolls seen, especially in the first game, can be more spread out so it doesn't appear to be as rigged.

In fact three throws makes it exceptionally simple to substitute in loaded dice, all the house would need to do would be to use three dice loaded towards the 6 for the first two throws and normal dice, or if the house was feeling particularly daring those loaded to the 1, for their obviously final throw. While the player may end up using the positively skewed dice every now and then, it would allow the house to significantly increase their odds over the player. This wouldn't be quite as simple in a game such as above where the controling player changes as the game progresses.

Then there is the statistical reason why the game wouldn't be played, if anyone actually tried to run a gambling establishment using a fair version of Chinchororin for revenue then they wouldn't be able to cover their overheads as detailed below. Even Marco's cup game favours the house and would be profitable if fair, without resorting to the rigged set-up such games usually tend to follow; this is not the case for Chinchororin if played on a one-to-one basis seen in the games.

Chinchororin: a Statistical Analysis

There are three dice in Chinchororin and so there are 6*6*6=216 different permutations of those 3 dice leading to the following probabilities:
  • Probability of a specific treble = 1 out of 216
  • Probability of 1-2-3 = 6 out of 216
  • Probability of 4-5-6 = 6 out of 216
  • Probability of a double and an x = 15 out of 216 where x = 1,...,6
  • Probability of no scoring result = 108 out of 216 = 1 out of 2

While I could spend a few pages detailing the exact formulas for every single calculation giving a step by step guide to how they were worked out and why most of the entries actually cancel I don't think I would hold the attention of anyone still reading this.

Instead I'll restrict this to the results and the obvious common sense way they are explained; but in order to do this I need to make a definition. In statistics when dealing with gambling games there is a value quoted for the game called its Expectation this is defined as the amount you would get back for every unit you bet and is calculated by multiplying the prize for each outcome by the probability for that outcome and adding them all together.

So for instance if the bet was on a fair coin toss where you get double the stake for guessing correctly and nothing for getting it wrong the expectation would be given by E=0*p(w)+2*p(C) since both probabilities are a half then the expectation is 1. Hence if you continued playing for a while you would expect to leave with exactly the same amount of money that you started with.

But Chinchororin is a bit more complicated than a coin toss, firstly we'll ignore the possibility of the dice landing outside the bowl and assume for the moment that each throw is on target.

Because we are looking at expectation the probability that anything comes up a draw and the stake is returned isn't an issue if we look at the difference between the stake and the expectation so that is the route we will take. Nor as it happens is any of the 1-2-3 or 4-5-6 results as they will pair off and cancel. As the dice always land in the bowl it is an obvious extension that the chance of one player gaining a higher double than the other will be the same for both players so the single multiple results will also cancel.

This leaves the only part of the equation not to cancel occurring being those related to the triples and thus the 3x stake outcomes. The reason these do not cancel is because they do not pair off and chance for the player to get a triple is conditional on the house not getting a triple or a 1-2-3/4-5-6 result first.

The probability of any player getting a triple in the three rolls works out as 7/864. The probability that the house gets 1 triple or 1-2-3/4-5-6 is 7/48.

Hence since there are five results for one side and one against then the difference is amounts won is given by:
3 * (5-1) * ( (1-7/48) -1) * 7/864 = 49/3456 = -0.0148 (3sf)

Thus the house would get 1.48% of the stake, or the expectation per unit stake is a return of 0.986. Thus for every 1000 potch/bits gambled the player should expect to get 986 potch/bits back.

But what of the assumption of always landing in the bowl, well common sense says that it will sometimes bounce out. However common sense also tells us that the person who makes the most rolls will be most affected by this instant lose outcome. In fact if each player misses the bowl 1 in every 20 rolls then the difference almost cancels out and the expectation becomes 99.9%.

Probability and the Suikoden games

It is fairly clear from the above that if they played fair no professional gambler, such as Shilo or Gaspar, could make enough money to live on if they made any money at all. As a game tends to its expectations after many plays, the casual player may win or lose so it is likely only the house that ends up in a break even position; unless the player plays for quite some time. As such for the sake of realism, the house should actually be expected to try and cheat using every trick possible so they would stay in profit.

Neither game follows the probabilities very closely. the first game mainly took its results from the total luck statistic of the party, and as such Gaspar was an exceptionally easy source of money, this is especially borne out in the way that a triple or 1-2-3/4-5-6 happened every two or three rolls instead of the more unlikely one in eighteen chance it should be. Maybe he keeps playing with the wrong set of loaded dice.

As for Shilo, well he is closer to the fair statistics than is usually claimed, as most of the time you end up breaking even after playing for a while. This belief is generally because he is not an easy source of cash the way Gaspar was, as it is hard to end up with anything resembling a big win. Whether party luck values play a part in this version of Chinchororin is debatable; although you don't see a triple or 1-2-3/4-5-6 quite as often as with Gaspar they do occur with more regularity than they statistically should. The conclusion to this is Shilo is a more shrewd gambler than Gaspar knowing when to use the loaded dice, and that you have to let the player win every so often.