How to gamble against all odds

Bienvenu, 2012, How powerful are integer-valued martingales?, Theory Comput. Syst., 51, 330, 10.1007/s00224-011-9362-3 Buss, 2013, Probabilistic algorithmic randomness, J. Symbolic Logic, 78, 579, 10.2178/jsl.7802130 Chalcraft, 2012, How to build a probability-free casino, Inform. Comput., 211, 160, 10.1016/j.ic.2011.12.004 Downey, 2007, Algorithmic randomness, Scholarpedia, 2, 2574, 10.4249/scholarpedia.2574 Hu, 2014, Unpredictability of complex (pure) strategies, Games Econ. Behav., 88, 1, 10.1016/j.geb.2014.08.002 Hu, 2013, Expressible inspections, Theoretical Econ., 8, 263, 10.3982/TE992 Peretz, 2015, Effective martingales with restricted wagers, Inform. Comput, 10.1016/j.ic.2015.10.001 Schnorr, 1971, A unified approach to the definition of random sequences, Math. Syst. Theory, 5, 246, 10.1007/BF01694181 Teutsch, 2013, A savings paradox for integer-valued gambling strategies, Int. J. Game Theory, 43, 145, 10.1007/s00182-013-0377-7 V'yugin, 2009, A on calibration error of randomized forecasting algorithms, Theoretical Comput. Sci., 410, 1781, 10.1016/j.tcs.2009.01.010