RU2142310C1 - Method for determining random playing factor (versions) - Google Patents

Abstract

FIELD: entertaining equipment, in particular, games such as dice. SUBSTANCE: method involves generating by one random signal from N ≥ two different groups of equally probable discrete whole number (including zero) random signals satisfying ratio, in which whole number random signal in group of signals and number of different values of random signals in group of signals are taken into account; determining the value of playing factor on the base of obtained combination of random signals by summing up values of generated random signals. Method allows range of values of discrete distribution of top boundary of range of possible values of random playing factor to be widened and interval between mentioned values to be reduced. EFFECT: simplified method and wider range of usages of method. 3 cl, 17 dwg

Description

 The invention relates to the field of games, and more particularly to methods for generating random numbers, mainly for dice games.

 From the prior art it is known that attempts have been made to create alternative methods for determining equiprobable gaming performance for dice.

 Thus, there is a known method for determining a random game indicator (US, N 4678190, A 63 F 9/04, 1987), which includes the formation of six different groups of six basic equally probable random signals in each group, the generation of one random signal from each group of basic equally probable random signals, each of which is a combination of two or three integers, and a random game score from 6 to 36 or from 6 to 49 is determined based on the resulting set of random basic signals.

 The disadvantages of this method are: a narrow range of variation of the values of a random game indicator, a large number of groups of basic equiprobable random signals, as well as the complex structure of each basic equiprobable random signal. As a consequence, the known method has a limited scope.

 There is also a method of determining a random game indicator (US, N 4743025, A 63 F 9/04, 1988), taken as a prototype and including the formation of several identical groups of six basic equally probable random signals in each group, the generation of one random signal from each groups of basic equally probable random signals, each of which is a single integer from 1 to 6, and a random game indicator is determined based on the resulting set of random basic signals.

 The main disadvantage of the known method for determining a random game indicator is that the upper value of the range of possible values of a random game indicator can only change with a very large factor of six (36, 216, 1296, etc.), which significantly limits the scope of use of the known way. In addition, the very definition of a random game indicator based on the obtained set of random basic signals is a laborious operation, since it involves the use of special tables, as well as special encoding of signals corresponding to different groups of basic signals.

 The present invention is directed to solving the technical problem of expanding the plurality of values of the discrete distribution of the upper boundary of the range of possible values of a random game indicator while reducing the interval between the above values. The technical result achieved in this case is to expand the field of use of the proposed method.

где C_n ^j - j-й целочисленный случайный сигнал в n-й группе сигналов (n = 1,2,...,N);
P_i ≥ 2 - число различных значений случайных сигналов в i-й группе сигналов (i = 1,2,...,n-1);
k_n ^j - коэффициент, принимающий значения 0,1,2,...,(P_n - 1) соответственно при j = 1,2,3,...,(P_n;

m - любое наперед заданное число от 1 до N;
а случайный игровой показатель, имеющий значение от 1 до

, определяют путем суммирования значений N генерированных случайных сигналов.The task, according to the first embodiment, is solved in that in the method for determining a random game indicator, according to which one random signal is generated from each finite group of equally probable discrete integer random signals, and based on the obtained set of random signals, a random game indicator is determined according to the invention, generate one random signal from N ≥ 2 different groups of equally probable discrete integer numbers, including zero, random signals, satisfying their ratio

where C _n ^j is the j-th integer random signal in the n-th signal group (n = 1,2, ..., N);
P _i ≥ 2 - the number of different values of random signals in the i-th signal group (i = 1,2, ..., n-1);
k _n ^j - coefficient taking values 0,1,2, ..., (P _n - 1), respectively, with j = 1,2,3, ..., (P _n ;

m is any predetermined number from 1 to N;
and a random game score that has a value from 1 to

are determined by summing the values of N generated random signals.

The discrete function δ _{mn was} first introduced by P. Dirac (see P. Dirac, Principles of Quantum Mechanics, trans. From the 4th English edition, M., Nauka, 1979, p. 89).

где C_n ^j - j-й целочисленный случайный сигнал в n-й группе сигналов (n = 1,2,...,N);
P_i ≥ 2 - число различных значений случайных сигналов в i-й группе сигналов (i = 1,2,...,n-1);
k_n ^j - коэффициент, принимающий значения 0,1,2,...,(P_n - 1) соответственно при j = 1,2,3,...,(P_n;

а случайный игровой показатель, имеющий значение от 1 до

определяют путем суммирования значений N генерированных случайных сигналов.According to the second embodiment, the problem is solved in that in the method for determining a random game indicator, according to which one random signal is generated from each final group of equally probable discrete integer random signals, and based on the obtained set of random signals, a random game indicator is determined, according to the invention, one random signal from N ≥ 2 different groups of equally probable discrete integer numbers, including zero, random signals, satisfying s relationship

where C _n ^j is the j-th integer random signal in the n-th signal group (n = 1,2, ..., N);
P _i ≥ 2 - the number of different values of random signals in the i-th signal group (i = 1,2, ..., n-1);
k _n ^j - coefficient taking values 0,1,2, ..., (P _n - 1), respectively, with j = 1,2,3, ..., (P _n ;

and a random game score that has a value from 1 to

determined by summing the values of N generated random signals.

The advantage of the proposed method is that due to the implementation of a set of new conditions for the implementation of known operations for generating random signals, namely:
- the presence of N ≥ 2 different groups of equally probable discrete integer random signals (basic signals),
- the presence in each group of at least two or two subgroups of equally probable discrete integer, including zero, signals having different values (P _i ≥ 2),
- the presence of a one-to-one correspondence between the group number of equally probable discrete integer random signals and the integer values of the signals in the corresponding group (dependence [1] or [2]),
the set of values of the discrete distribution of the upper boundary of the range of possible values of the random game indicator is expanded, which is now determined by the expression [2 ^α × 3 ^β × 4 ^γ × 5 ^ξ × 6 ^ε × ...] for the first embodiment of the method or the expression [(2 ^α × 3 ^β × 4 ^γ × 5 ^ξ × 6 ^ε × ...) - 1] - for the second option, while α, β, γ, ξ, ε, ... are any integers, including zero, satisfying the condition α + β + γ + ξ + ε + ... = N. Moreover, there is no need for additional coding of signals corresponding to the same group. Thus, the smallest upper value of the range of possible values of a random game indicator is not 36, as in the prototype, but 4 (α = 2 = N), while there are no restrictions from above. In addition, the interval between adjacent upper values of the range of possible values of a random game indicator is narrowed significantly. Indeed, for representing undoubtedly practical interest case P _i = 2, 3 and 6, a plurality of upper value range of possible values of the random gaming indicator set includes all integers except simple and multiple them.

 It is advisable in some cases that the game indicator has a zero value. The second embodiment of the proposed method demonstrates this possibility.

 Thus, the achievement of the technical result, which consists in expanding the field of use (indoor games, gambling, mass entertainment) of the method for determining a random gaming indicator.

 Further, the invention is illustrated by drawings and description thereof.

 In FIG. 1 shows a block diagram of a device for implementing the proposed method; in FIG. 2, 3, 4, and 5 — sweeps in the plane of the first, second, third, and fourth hexagonal dice, respectively, for values of a random game indicator from 1 to 36; in FIG. 6 and 7 - sweeps in the plane of the first and second tetrahedral dice, respectively, for values of a random game indicator from 1 to 36; in FIG. 8, 9 and 10 - sweeps in the plane, respectively, of the first and second hexagonal and third - tetrahedral dice for values of a random game indicator from 1 to 36; in FIG. 11 and 12 - sweeps in the plane of the first and second hexagonal dice, respectively, for values of a random game indicator from 1 to 36; on Fig 13 and 14 - scan in the plane, respectively, of the third and fourth hexagonal dice for values of a random game indicator from 1 to 1296; in FIG. 15, 16 and 17 - sweeps in the plane of the first, second and third hexagonal dice, respectively, for values of a random game indicator from 0 to 215.

A device for implementing the proposed method comprises an N-input adder 1, N blocks 2 ¹ - 2 ^N memory, N multiplexers 3 ¹ - 3 ^N , N generators 4 ¹ - 4 ^N uniformly distributed random binary numbers, a start block 5 and an indicator 6. Blocks 2 ¹ - 2 ^N memory have corresponding inputs 7 ¹ - 7 ^N , and the outputs of each block 2 ¹ - 2 ^N memory are connected to the information inputs of the corresponding multiplexer 3 ¹ - 3 ^N. The outputs of each generator 4 ¹ - 4 ^{N are} connected to the address inputs of the corresponding multiplexer 3 ¹ - 3 ^N , the outputs of which are connected to the corresponding inputs of the N-input adder 1. The output of the N-input adder 1 is connected to the input of the indicator 7, and the output of the trigger unit 5 is connected with the control inputs of the generators 4 ¹ - 4 ^N uniformly distributed random binary numbers.

 In addition, the drawings indicate the development of 8-23 dices having four or six faces.

 The proposed method is as follows.

Preliminarily, based on the required range of variation of a random game indicator, the number of groups of equally probable discrete integer signals is determined. To do this, set such values of exponents in the expression [2 ^α × 3 ^β × 4 ^γ × 5 ^ξ × 6 ^ε × ...] (3) if the lower boundary of the above range is equal to unity, for which the expression in square brackets is equal to the upper the boundary of the range of variation of a random game indicator. For example, for the upper boundary equal to 1296, the expression in square brackets can be represented as follows: [2 • 3 ³ • 4 • 6]. In other words, α = 1, β = 3, γ = 1, ξ = 0, ε = 1, and the remaining exponents are zero. The sum of the exponents (α + β + γ + ε) is the number of different groups N = 6 equally probable discrete integer random signals, and 2, 3, 4, and 6 are the number of non-repeating signals in the first (second, third, and fourth, respectively, since β = 3), as well as in the fifth and sixth groups. Further, in accordance with relation (1), the values of equiprobable discrete integer random signals (groups of basic signals) are calculated. After that, the input 7 ¹ in the block 2 ¹ memory records the values of the integer signals of the first group. At the input 7 ² in the block 2 ² memory values are written integer signals of the second group. And so on. After that, by the “Start” command, a control pulse is generated at the output of the start-up block 5, which starts the generator, 4 ¹ - 4 ^N evenly distributed random numbers. At the end of the control pulse, signals corresponding to the generated random numbers appear at the outputs of the generators 4 ¹ - 4 ^N. These signals from the outputs of the generators 4 ¹ - 4 ^N are fed to the address inputs of the corresponding multiplexers 3 ¹ - 3 ^N. At the same time, at the output of each multiplexer 3 ¹ - 3 ^{N, a} signal appears from that information input, the number of which corresponds to a binary number (code) at its address inputs. Since the information inputs of each multiplexer 3 ¹ - 3 ^{N are} fed with signals recorded in the cells of the corresponding block 2 ¹ - 2 ^N memory, the outputs of the N-input adder 1 will be fed with signals generated randomly from each group of basic signals. Thus, at the output of the adder 1, a signal appears, the value of which will correspond to a random game indicator.

 The formation of the next game indicator is carried out by submitting a second start command to the launch unit 5.

If the lower bound of the range of values of a random game indicator is equal to zero, then instead of expression (3), the expression [(2 ^α × 3 ^β × 4 ^γ × 5 ^ξ × 6 ^ε × ...) - 1] is used (4). The remaining actions are similar to those described above.

 In addition to the means described above, for the implementation of the proposed method, at least two (since N ≥ 2) dices can be used, for example, the most commonly used dice. In this case, digital information marks applied to the edges of the same dice form a group of equally probable discrete integer random signals (basic), and those that have fallen as a result of throwing bones (using any of a number of known devices, for example, described in GB- patents 1-2145638, GB-A-2195089) digital information labels form a set of N generated random signals, which determine (by summing the values of the generated signals) the value of a random game indicator.

 Depending on the required range of possible values of a random game indicator, the required number of dice (various groups of equally probable discrete integer random signals) is determined, as well as the values of the above signals in accordance with expressions (1) or (2).

Example 1. For the upper value of the range of possible values of a random game indicator equal to 36, the following three options are possible for P _i = 2,3,4,6:
1) 2 ² • 3 ² = 36; 2) 3 ² • 4 = 36; 3) 6 ² = 36.

In the first case, four bones are required (α = 2, β = 2, α + β = N = 4); in the second case, three bones (β = 2, γ = 1, β + γ = N = 4), and in the third, two bones (ε = 2 = N).
Let the lower value of the range of possible values of a random game indicator be equal to one. In this case, integer random signals in each group are determined from relation (1). For m = 1 has for the first case:
n is 1; C ₁ ¹ = 1; C ₁ ² = 2;
n is 2; C ₂ ¹ = 0; C ₂ ² = 2;
n is 3; C ₃ ¹ = 0; C ₃ ² = 4; C ₃ ³ = 8;
n is 4; C ₄ ¹ = 0; C ₄ ² = 12; C ₄ ³ = 24.

In the case of using hexagonal bones, the total number of equally probable random signals in each group of signals is equal to the number of faces of the dice, in other words, six. To ensure equal probability for two different signals, a group of six equally probable random signals should contain two subgroups of signals, the first subgroup containing three identical signals C ₁ ¹ or C ₂ ¹ , and the second subgroup also containing three identical signals C ₁ ² or C ₂ ¹² (Figs. 2 and 3). Similarly, to ensure equal probability for three different signals (n = 3, 4), a group of six equally probable random signals should contain three subgroups of two identical signals (0, 0, 4, 4, 8, 8 for n = 3) and (0 , 0, 12, 12, 24, 24 for n = 4), as shown in FIG. 4 and 5. Instead of hexagonal bones for n = 1 and n = 2, tetrahedral dice can also be used. In this case, each subgroup will contain two identical signals (Fig. 6 and 7).

In the second case, for m = 2, we have the following three groups of equally probable random signals:
n is 1; C ₁ ¹ = 0; C ₁ ² = 1; C ₁ ³ = 2;
n is 2; C ₂ ¹ = 1; C ₂ ² = 4; C ₂ ³ = 7;
n is 3; C ₃ ¹ = 0; C ₃ ² = 9; C ₃ ³ = 18; C ₃ ⁴ = 27.

 In this case, hexagonal dice (Figs. 8 and 9) are used to generate random signals of the first and second groups (n = 1, 2) of signals (Fig. 8 and 9), and tetrahedral dice is used for signals from the third group (Fig. 10).

In the third case, for m = 1, we have the following two groups of equally probable random signals:
n is 1; C ₁ ¹ = 1; C ₁ ² = 3; C ₁ ³ = 3; C ₁ ⁴ = 4; C ₁ ⁵ = 5; C ₁ ⁶ = 6;
n is 2; C ₂ ¹ = 0; C ₂ ² = 6; C ₂ ³ = 12; C ₂ ⁴ = 18; C ₂ ⁵ = 24; C ₂ ⁶ = 30;
for the generation of which two hexagonal bones are used (Figs. 11 and 12). The use of dice with a number of faces greater than six does not seem appropriate, since the use of only four hexagonal bones provides the upper value of the range of variation in the value of the random game indicator, equal to 1296, which is quite enough in the vast majority of cases. In FIG. 11-14 show sweeps in the plane of four hexagonal dice for a range of variation of a random game score from 1 to 1296.

Example 2. In the case when the lower value of the range of possible values of a random game indicator is equal to zero, integer random signals in each group are determined from relation (2). One of the possible options for implementing the range of variation of a random game indicator from 0 to 215 is a set of three groups of equally probable random signals (ε = 3 = N):
n is 1; C ₁ ¹ = 0; C ₁ ² = 1; C ₁ ³ = 2; C ₁ ⁴ = 3; C ₁ ⁵ = 4; C ₁ ⁶ = 5;
n is 2; C ₂ ¹ = 0; C ₂ ² = 6; C ₂ ³ = 12; C ₂ ⁴ = 18; C ₂ ⁵ = 24; C ₂ ⁶ = 30;
n is 3; C ₃ ¹ = 0; C ₃ ² = 36; C ₃ ³ = 72; C ₃ ⁴ = 108; C ₃ ⁵ = 144; C ₃ ⁶ = 180.

 Since each group contains six equally probable random signals, then three hexagonal dice are required to implement the above range of variation of the random game indicator (Figs. 15-17).

 The proposed method can be used when conducting indoor games, including gambling, and various mass entertainment, in particular express lotteries, either in specially equipped stationary or mobile rooms, or in the open air, for example, in amusement parks.

Claims (2)

1. A method for determining a random game indicator, according to which one random signal is generated from each final group of equally probable discrete integer random signals, and based on the obtained set of random signals, a random game indicator is determined, characterized in that one random signal is generated from N ≥ 2 various groups of equiprobable discrete integers, including zero, random signals satisfying the relation

where C ^j _n is the j-th integer random signal in the n-th signal group (n = 1, 2, ..., N);
P _i ≥ 2 - the number of different values of random signals in the i-th group of signals (i = 1, 2, ..., n-1);
K $\genfrac{}{}{0ex}{}{\text{j}}{\text{i}}$ - coefficient taking values 0, 1, 2, ..., (P _n - 1), respectively, for j = 1, 2, 3, ..., P _n ;

m is any predetermined number from 1 to N,
and a random game score that has a value from 1 to

determined by summing the values of N generated random signals. 2. A method for determining a random game indicator, according to which one random signal is generated from each final group of equally probable discrete integer random signals, and based on the obtained set of random signals, a random game indicator is determined, characterized in that one random signal is generated from N ≥ 2 various groups of equiprobable discrete integers, including zero, random signals satisfying the relation

where C ^j _n is the j-th integer random signal in the n-th signal group (n = 1, 2, ..., N);
P _i ≥ 2 - the number of different values of random signals in the i-th group of signals (i = 1, 2, ..., n-1);
K $\genfrac{}{}{0ex}{}{\text{j}}{\text{n}}$ - coefficient taking values 0, 1, 2, ..., (P _n - 1), respectively, for j = 1, 2, 3, ..., P _n ;

and a random game score that has a value from 0 to

determined by summing the values of N generated random signals.

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