Dice It is the earliest Gambling One of appliances. In this article I will discuss only the standard of modern dice. Such natural dice are cubes, each side has a number of points, which points 1,2,3,4,5 and 6 respectively on opposite sides on the number of points and was 7, 6 face this dice can be divided into three pairs, namely 1 and 6,2 and 5,3 and 4. dice face exactly two configurations of this nature, and this two ways to mirror each other. At present, almost all Western-built three dice faces 1,2,3-clockwise direction along the road around their common vertex arrangement. Someone told me that in Japan, having such All hand throwing dice for the addition of Mahjong Game In Mahjong this game using dice and their mirror images, from now on, unless otherwise indicated, I will use the western dice.
Often paired throw dice in order to obtain a desired total number of points. First, assume the dice are "fair", each side has a 1/6 probability throw when this probability in order to calculate a total number of points arise, we We must find out how many situations you can get the total number of points. Then we divide this figure by 36, that is, the total number of dice pair (Note that you must distinguish the two dice).
Imagine a dice are red and the other blue dice helps to understand the problem. Thus, for example, 12 of the total number of points can have a situation where the red dice roll 6:00, and 6:00 blue dice are thrown. Therefore, the probability of 12 total points to the emergence of 1/36. In addition, a total of 11 points can be obtained in two circumstances, namely red dice roll 6:00, 5:00 blue dice roll, or red dice roll 5:00, 6:00 blue dice roll. Thus the probability of 11 total points to the emergence of 2/36, namely 1/18.
The great mathematician and philosopher Gottfried Leibniz believes throw 11:00 and 12:00 probability must be the same, because in his view there is only one case thrown 11 total points eleven this is a dice roll 6 points, while another dice roll 5:00. There are several problems in this theory. Perhaps the most prominent problem is that it is completely contradictory with the experimental results. The results show the possibility of the throw to throw 11:00 12:00 possibility of . twice Another problem is that this theory would lead to an unreliable conclusion that the two dice roll a total points - no matter how much - the probability is less than 1.
In there is a gambling game throw two dice (craps), the intuitive sense of these probabilities plays a key role.Throw two dice gambling originated in the 1840s.In this gambling, a Candu (dice party) took a sum of money at stake.Other Candu then "follow" (fade), that is their choice bet a sum of money.If the amount is less than the money follow the dice has commenced bet nowadays, he put the bet and the total reduction to equal.Then dice throw a pair of dice has commenced.If the first throw of the dice total 7 or 11 points (called "natural" points (natural)), then he immediately won the gamble.If the total number of points of the first throw of the dice is 2, 3 or 12 ("craps"), then he lost the gamble.In other cases, the first to throw the dice party's total number of points - ie 4,5,6,8,9 or 10-- is their "score".In this case he must continue to throw down, and strive to throw a score again, and then throws a 7 ("craps out").If you can throw such a result, he will win all bets, otherwise he would lose our shirts.
According to various probabilities previously mentioned as well as the rule of gambling, you can calculate the chance of winning dice party 244/495, that is about 49.3%. This is an equal opportunity than winning probability (50%) just smaller Vocational gambler can be two ways to this tiny disadvantage into advantage. One approach is to accept or reject various other Candu "collateral bet" (ie more than the general ante bet) Another The method is a fraud, gambling used to deceive the public gimmicky use of rigged dice.
There are several ways you can play tricks on the dice.Each face of the dice can be cleverly cut repair, so that their respective corners not at right angles, can also be used to weight the dice "irrigation lead".Both methods can throw some dice points more likely than others Points.Fraud more dramatic approach is to use the "top roll" (top) and "bottom dice" (bottom) instead of the standard dice.Two on each side of the dice only three different points (opposite faces of the same number of points each).Because any one Candu at any time can only see up to 3 faces of a dice, and all adjacent faces are not the same number of points, so it did not seem at first glance unusual happens.However, it is impossible to ensure that all surfaces are arranged in a standard order on all the vertices.In fact, if the number of points on the surface of a vertex of three 1,3,5 arranged pick counterclockwise direction, then in the adjacent three faces will surely these are arranged in a clockwise direction on the vertex.
In throwing craps gambling, the top and bottom dice dice can be used to achieve a variety of different purposes. For example, using a pair of 1-3-5 dice, will never throw 7 the total number of points, so use this type of dice a Candu will never win (crap out). to a 1 a 3-5 dice and a dice together with 2-4-6, you can not obtain even the total number of points, so use this two A Candu impossible dice throw 4,6,8 or 10 total points if these acts are not cheating to make these people aware, then the use of non-top dice too much - as always throw an even number The total number of points, so even the most inexperienced of Candu will be suspicious of.
Many tricks or a party trick play uses dice.A significant advantage of the relative number of tricks each side of the dice points and 7 this rule.Martin Garner in his book "Math Magic" introduces a trick.Magician turned away, please an audience throwing three standard dice, then put up the number of points for each plane together.Then please magician who fooled pick up any one of the dice, put it down side is applied to the total number of points obtained earlier.Finally, the audience put the dice roll once again, the upward side of the points plus the total number on the second (he must own to remember all these totals).Now magician turned back, casually reported result is how much, though she did not know that viewers choose which one dice.
Wonders where? Assume these dice up side points were a, b and c, and the concept of choice is a dice. The initial sum is a + b + c, plus the sum of the 7-a, you get b + c + 7. Then a dice again throw once, resulting points to d, so the final result is d + b + c + 7. Then the magician look at these three dice, sum them up side of the Points of d + b + c, so the magician only quickly these three numbers add up to plus 7're done.
British puzzle expert Henry Ernest Dudene, in his book (fun math) introduces a different trick.Magic still turned away, please an audience threw dice.But now she is let the people who were fooled the first dice multiplied by 2 plus 5, this result is multiplied by 5 after the first two dice roll plus points, followed by 10 and then multiply the result by this the last throw of the dice plus the first three points.After learning of this result, the magician immediately reported three dice throw of the number of points each.Natural final result obtained is the viewer 10 (5 (2a + 5) + b) + c, i.e., 100a + 10b + c + 250.Therefore magician simply subtracted from this result in 250, the remaining three-digit three figures are the three points of the dice throw.Other dice problem involves some changes of the dice, they have a nonstandard points.For example, if the reader can come up with a way to use only these numbers 0,1,2,3,4,5 or 6 to a pair of dice to the provisions of points, which makes the total number of points after the throw of the dice and all the various possible scenarios as big chance (from 1-12) appears (see answer at the end of this article)?Perhaps the most substandard human intuition dice phenomenon is called "non-delivery of the dice.".Do three dice A, B, C, of its surface points are as follows:
A: 334488 B: 115599 C: 226677
Many times after the throw, throw the dice B points better than average, would throw the dice A number of points.In fact, the probability of a large number of points dice throw points B than A throw of dice 5/9.Similarly, the probability of a large number of points C throw dice points than throw of the dice for B 5/9.Then throw the dice C points on average Obviously the big points A throw ratio, right?No, on the contrary, the probability of a large number of points A throw of dice points than dice throw of 5/9 C.Drawing out the rationale for the above statement of.You can use this set of dice jackpot! Let your gambling opponents to pick any one of the dice, then you choose a can overwhelm its dice (throwing many times later, the probability of your opponents dice dice than greater than l / 2) and then go on repeating such bet.You will be in all 55 bet.55% win.But your opponents have the freedom to choose his considered the "best" dice!