Testing Randomness: Poker Test with Hands of Three Numbers

Problem statement: The problem of testing randomness is motivated by the need to evaluate of the quality of different random number generators used by many practical applications including computer simulations, cryptography and communications industry. In particular, the quality of the randomness of the generated numbers affects the quality of such applications. In this study we focus on one of the most popular approaches for testing randomness, Poker test. Two versions of Poker test are known: the classical Poker test and the approximated Poker test, where the latter has been motivated by the difficulties involved in implementing the classical approach at the time it is designed. Approach: Given a sequence of n random numbers to be tested, the basic Poker approach divides this sequence into groups of k = 5 numbers, observes which of the possible patterns is matched by each quintuple, computes the occurring probability of each of these patterns and finally applies Chi-square test to check the randomness of such sequence. Results: For the sake of efficiency of the test, it is shownin the literature that, the value of k should be bounded from above based on the number of random numbers n to be tested On the other hand, most practical applications apply poker test with different values of k in order to ensure that the underlying sequence is truly random. This motivates implementing Poker approach with hands of three numbers in this study. Conclusion: We discuss the Poker test with hands of three numbers optimized for testing the randomness of sequences of sufficiently small sizes. From the computations point of view, we compare the performance of implementing Poker approach that uses hands of three, four, and five numbers and show that the running time of implementing the hands of three numbers is close to that hands of four numbers and is significantly less than that hands of five numbers.