Algorithmic randomness and splitting of supermartingales
An. A. Muchnik · Problems of Information Transmission · 2009
Randomness in the sense of Martin-Löf can be defined in terms of lower semicomputable supermartingales. We show that such a supermartingale cannot be replaced by a pair of supermartingales that bet only on even bits (the first one) and on odd bits (the second one) knowing all the preceding bits.