Statistical problem concerning session EV
I would appreciate help with a statistical problem of significance to some advantage gamblers (especially online bonus hustlers). 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. One might also discern that the magnitide of the difference between the two player's EV's would be positively correlated with both variables "X" and "Y".
How would one calculate the difference between the session EV's of these two players?
-PG
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