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Using biased coins as oracles
, 2004
"... Abstract. While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set X may be coded as a probability pX such that if a Turing machine is given a ..."
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Cited by 4 (3 self)
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Abstract. While it is well known that a Turing machine equipped with the ability to flip a fair coin cannot compute more that a standard Turing machine, we show that this is not true for a biased coin. Indeed, any oracle set X may be coded as a probability pX such that if a Turing machine is given
THE CONTROLLED BIASED COIN PROBLEM
"... Abstract. We study the maxmin value of a zerosum repeated game where player 1 is restricted to pure strategies but privately observes the realizations of some random variables. This kind of problem was introduced by Gossner and Vieille [GV02] in the case where player 1 observes i.i.d. random variab ..."
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variables. The paper solves the case where the law of the random variable (the coin) depends on player 1’s action. We also discuss the general case where the law of the coin is controlled by both players. 1. Model and definitions 1.1. The repeated game. Let (A,B, g) be a zerosum game where, A (resp. B
Efficient Simulations by a Biased Coin
 Information Processing Letters 56
, 1995
"... this paper, bias is a rational number between 0 and ..."
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Cited by 2 (1 self)
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this paper, bias is a rational number between 0 and
Efficient Generation of Fair Dice with Few Biased Coins
"... Given a random variable X which takes n equiprobable values, we consider several algorithmic questions related to the classical problem of simulating the outcomes of X by using a limited number of biased coins. Index terms: Randomized algorithms, random number generation, biased coins. Work suppor ..."
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Cited by 1 (0 self)
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Given a random variable X which takes n equiprobable values, we consider several algorithmic questions related to the classical problem of simulating the outcomes of X by using a limited number of biased coins. Index terms: Randomized algorithms, random number generation, biased coins. Work
The Distribution of Loss in TwoTreatment BiasedCoin Designs
, 2002
"... The paper compares randomised rules of the biasedcoin type for the sequential allocation of treatments in a clinical trial. An important characteristic is the loss, which measures the increase in the variance of parameter estimates due to the imbalance caused by randomisation. Simulations are used ..."
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Cited by 1 (0 self)
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The paper compares randomised rules of the biasedcoin type for the sequential allocation of treatments in a clinical trial. An important characteristic is the loss, which measures the increase in the variance of parameter estimates due to the imbalance caused by randomisation. Simulations are used
Finding a most biased coin with fewest flips
, 2014
"... We study the problem of learning a most biased coin among a set of coins by tossing the coins adaptively. The goal is to minimize the number of tosses until we identify a coin whose posterior probability of being most biased is at least 1 − δ for a given δ. Under a particular probabilistic model, we ..."
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Cited by 2 (0 self)
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We study the problem of learning a most biased coin among a set of coins by tossing the coins adaptively. The goal is to minimize the number of tosses until we identify a coin whose posterior probability of being most biased is at least 1 − δ for a given δ. Under a particular probabilistic model
ON BIASED COIN TOSSING AND CYCLIC RANDOM WALKS
"... Imagine that you and some friends are playing a version of roulette. The wheel is divided into 36 sectors, alternately colored red and black. Before spinning the wheel, the contestant chooses a color and then wins or loses depending on whether or not his color comes up. You, the master player, have ..."
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if his guess matches the final outcome that he wins the game. Is this fellow on to something? Will the new rule blunt your advantage? Let us assume that you continue to bet on the wheel’s starting color, and think of each spin as a coin toss in which the probability of ‘heads ’ is 0.9 (i.e., the wheel
Predicting a Binary Sequence Almost as Well as the Optimal Biased Coin
, 1996
"... We apply the exponential weight algorithm, introduced and Littlestone and Warmuth [17] and by Vovk [24] to the problem of predicting a binary sequence almost as well as the best biased coin. We first show that for the case of the logarithmic loss, the derived algorithm is equivalent to the Bayes alg ..."
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Cited by 50 (5 self)
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We apply the exponential weight algorithm, introduced and Littlestone and Warmuth [17] and by Vovk [24] to the problem of predicting a binary sequence almost as well as the best biased coin. We first show that for the case of the logarithmic loss, the derived algorithm is equivalent to the Bayes
Printed in Great Britain The distribution of loss in twotreatment biasedcoin designs
"... The paper compares randomized rules of the biasedcoin type for the sequential allocation of treatments in a clinical trial. An important characteristic is the loss, which measures the increase in the variance of parameter estimates due to the imbalance caused by randomization. Simulations are used ..."
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The paper compares randomized rules of the biasedcoin type for the sequential allocation of treatments in a clinical trial. An important characteristic is the loss, which measures the increase in the variance of parameter estimates due to the imbalance caused by randomization. Simulations are used
Results 1  10
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79,706