People are risk averse, so a zero-sum bet (in money) would have negative utility for the weaker player, unless the player causes the probability of winning to increase given a fixed bet (this is “application of skill”, that is performance with exceptionally good concentration/preparation/etc. that makes the a priori estimation of player’s skill inaccurate in the particular game). The amount on which this probability must be increased in order to make the expected utility of the bet positive, depends on the absolute values of bets. The bigger the bets, the more the weaker player must increase the probability of winning in order to cross over into positive expected utility.
A game can then be called “a game of skill” if effort can sufficiently increase player’s probability of winning, and “a game of luck” if an impossible increase in this probability is necessary. Normal lotteries can’t be turned to positive expected utility, so they are always games of luck. Poker can’t be turned to positive expected utility by weak players, so for them it’s game of luck, while for stronger players it’s game of skill. Chess for smaller bets is game of skill, and for bigger bets game of luck for the weaker player.
People are risk averse, so a zero-sum bet (in money) would have negative utility for the weaker player, unless the player causes the probability of winning to increase given a fixed bet (this is “application of skill”, that is performance with exceptionally good concentration/preparation/etc. that makes the a priori estimation of player’s skill inaccurate in the particular game). The amount on which this probability must be increased in order to make the expected utility of the bet positive, depends on the absolute values of bets. The bigger the bets, the more the weaker player must increase the probability of winning in order to cross over into positive expected utility.
A game can then be called “a game of skill” if effort can sufficiently increase player’s probability of winning, and “a game of luck” if an impossible increase in this probability is necessary. Normal lotteries can’t be turned to positive expected utility, so they are always games of luck. Poker can’t be turned to positive expected utility by weak players, so for them it’s game of luck, while for stronger players it’s game of skill. Chess for smaller bets is game of skill, and for bigger bets game of luck for the weaker player.