"Suppose Player A has a session bankroll of $100 and Player B has a session bankroll of $200. Both players will bet $5 per hand on the same randomly dealt videopoker game which has a house edge of X (a number between 0 and 100%) and a standard deviation of Y. Both players will bet on exactly 200 hands ($1000 in total wagers), unless they go bust before reaching 200 hands (in which case their gambling session will come to a premature end).
Since Player A's maximum potential loss is $100 less than the maximum potential loss of Player B, it should be clear that Player A will have a higher session EV (i.e., a smaller expected loss) than player B."
No, the EV is the same for both players, in both percentage and monetary terms. If, for example the house edge is X=1.5%, both players' EV for their first 200 hands is -1.5% of their total action; in other words (-1.5%)*($1000)=-$15.
"One might also discern that the magnitude of the difference between the two player's EV's would be positively correlated with both variables "X" and "Y"."
The only difference between the two players' "expectation", is that player A should "expect" to go bust with a higher probbaility than player B, since A has a lower Bankroll than B, and since they are both betting the same flat amount.
Please also note that X (:edge) and Y (:SD) are the same for both players, who are, thus, playing a game with the same Reward-to-Risk ratio.
For more on this important issue, skip the economic journals' lingo and head for
Don Schlesinger's "Blackjack Attack". Get the 2nd edition.