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As the two players in Square++ act on different roles, we apply a biased coin to make the game playing fair.
To fill this gap, we review six up-and-down designs: the "3 + 3" design, accelerated titration design, biased coin design, k-in-a-row design, group up-and-down design and cumulative group up-and-down design.
This paper develops a unified method to compute the exact statistical power for a general class of response adaptive designs including the randomized play-the-winner design, the drop-the-loser design, and the doubly biased coin design.
We propose that the base station chooses according to a geometric distribution given by for a chosen parameter (discussed further below)—the base station can implement this choice easily by simulating a (biased) coin toss.
Other means of restricted randomisation include replacement, biased coin, and urn randomisation, although these are used much less frequently.
To get a better feeling for this distinction, consider the experiment of tossing a biased coin having probability p of heads and q = 1 − p of tails until heads first appears.
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Adaptive randomization of the sequential construction of optimum experimental designs is used to derive biased-coin designs for longitudinal clinical trials with continuous responses.
The time of stick represents the fraction of time that the oscillator sticks, it can be viewed as the probability of a biased-coin problem: stick is head and slip is tail.
The randomization procedure used is a simple adaptive biased-coin randomization.
Treatment allocation is performed randomly by online application of a biased-coin randomization (minimization).
Balance of treatment counts is achieved by the biased-coin method with probability 0.7 [ 40].
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