In working with EV should we always be looking forward only?
i.e. if we worked out a 95% confidence interval for 300 hours of play and are now 100 hours through it, then surely it would be wrong to keep the confidence intervals at the end of the 300 hours constant?
for example:
assume EV= 2 units/hour SD=30 units/hour
EV = 300x2 = 600 units SD = SQRT(300)*30 = 520
with having zero completed hours we have 68% confidence interval = 600-520, 600+520 = +80,+1120
but after 100 hours we are actually up 350 units
in this case should we calculate our confidence interval for the 300 hours as follows (GIVEN that we already have a result for the first 100 hours)
EV = 350 (actual win) + 200x2 = 750
SD = SQRT(200) *30 =424
Thus confidence interval for 300 hours (where first 100 is already completed) is
750-424, 750+424 = +326,+1174
This is in essence saying that past results do not impact on future results i.e. we cannot expect our 300-hour 68% confidence interval to stay constant if we already have results for a portion of the 300 hour session. Or in other words the EV for the next 100 hours will always be the same regardless whether we have had 5 consecutive winning 100-hour sessions or 5 consecutive losing 100-hour sessions.
Am I understanding this correctly?
i.e. if we worked out a 95% confidence interval for 300 hours of play and are now 100 hours through it, then surely it would be wrong to keep the confidence intervals at the end of the 300 hours constant?
for example:
assume EV= 2 units/hour SD=30 units/hour
EV = 300x2 = 600 units SD = SQRT(300)*30 = 520
with having zero completed hours we have 68% confidence interval = 600-520, 600+520 = +80,+1120
but after 100 hours we are actually up 350 units
in this case should we calculate our confidence interval for the 300 hours as follows (GIVEN that we already have a result for the first 100 hours)
EV = 350 (actual win) + 200x2 = 750
SD = SQRT(200) *30 =424
Thus confidence interval for 300 hours (where first 100 is already completed) is
750-424, 750+424 = +326,+1174
This is in essence saying that past results do not impact on future results i.e. we cannot expect our 300-hour 68% confidence interval to stay constant if we already have results for a portion of the 300 hour session. Or in other words the EV for the next 100 hours will always be the same regardless whether we have had 5 consecutive winning 100-hour sessions or 5 consecutive losing 100-hour sessions.
Am I understanding this correctly?