  The prospects of Kahneman and Tversky, Mega Million and Powerball lotteries,
St. Petersburg paradox, premature profits and growing losses criticized by
Livermore are reviewed under an angle of view comparing mathematical
expectations with awards received. Original prospects have been formulated as a
one time opportunity. An award value depends on the number of times the game is
played. The random sample mean is discussed as a universal award. The role of
time in making a risky decision is important as long as the frequency of games
and playing time affect their number. A function of choice mapping properties
of two-point random variables to fractions of respondents choosing them is
proposed.
