$A$ and $B$ are gambling with 2 dice. If the roll results in an odd number of points, $A$ receives from $B$ an amount of forints equal to the number of points. If the roll results in an even number of points, however, $B$ receives from $A$ an amount of forints equal to the number of points, except if the roll is 2, in which case no one pays. Who has the advantage in this game, and what is the expected profit for the advantaged party after 36 rolls?
With two dice, the number of all possible throws is $6 \cdot 6=36$ (or $V_{6}^{i, 2}$). Out of these 36 throws, 2 (and 12) can occur in 1 way, 3 (and 11) in 2 ways, 4 (and 10) in 3 ways, 5 (and 9) in 4 ways, 6 (and 8) in 5 ways, and finally 7 in 6 ways.

Thus, the expected value of $A$'s winnings after one throw is

$$
\begin{aligned}
M_{A} & =\frac{2}{36} \cdot 3+\frac{4}{36} \cdot 5+\frac{6}{36} \cdot 7+\frac{4}{36} \cdot 9+\frac{2}{36} \cdot 11-\frac{3}{36} \cdot 4-\frac{5}{36} \cdot 6- \\
& -\frac{5}{36} \cdot 8-\frac{3}{36} \cdot 10-\frac{1}{36} \cdot 12=\frac{126}{36}-\frac{124}{36}=\frac{2}{36}=\frac{1}{18}>0
\end{aligned}
$$

Thus, the game is favorable to $A$, and the expected value of $A$'s winnings after 36 throws is

$$
36 \cdot \frac{1}{18}=2 \text{ Ft}
$$

Pogány Eörs (Bp. XI., József Attila g. II. o. t.)