Do you mean just simple replacement of $1000 entry fee with something larger? Then yes, there are such thresholds.
In this example, the first threshold would be at “Lose $4900”, because the predictor is only guaranteed to get it right (and not show you the button) at least 98% of the time. The button could appear up to 2% of the time, for which the weighted loss is $98. The other 98% of the time, the predictor would correctly predict your action and show you the “Win $100″ button for a weighted gain of $98. You have nothing (financial) to gain by entering the building now. If you do anyway (e.g. if you’re forced in), then you still lose less on average by committing to press the Lose button when it appears.
The next threshold is at “Lose $9900”, where the weighted loss is $198 vs weighted gain of $98. If you’re forced to enter the building, the average return from the strategy of pressing the Lose button when it appears may now be no better than pressing the yellow button (and losing $100) in that case, and may be slightly worse (because a strategy of pressing Yellow might be mispredicted and show you the Win button anyway).
If you have reason to believe that pressing the red Lose button will be mispredicted less than 2% of the time, then these thresholds will be greater.
Do you mean just simple replacement of $1000 entry fee with something larger? Then yes, there are such thresholds.
In this example, the first threshold would be at “Lose $4900”, because the predictor is only guaranteed to get it right (and not show you the button) at least 98% of the time. The button could appear up to 2% of the time, for which the weighted loss is $98. The other 98% of the time, the predictor would correctly predict your action and show you the “Win $100″ button for a weighted gain of $98. You have nothing (financial) to gain by entering the building now. If you do anyway (e.g. if you’re forced in), then you still lose less on average by committing to press the Lose button when it appears.
The next threshold is at “Lose $9900”, where the weighted loss is $198 vs weighted gain of $98. If you’re forced to enter the building, the average return from the strategy of pressing the Lose button when it appears may now be no better than pressing the yellow button (and losing $100) in that case, and may be slightly worse (because a strategy of pressing Yellow might be mispredicted and show you the Win button anyway).
If you have reason to believe that pressing the red Lose button will be mispredicted less than 2% of the time, then these thresholds will be greater.