Probability theory

[hypercube]

no this is wrong the ev of switching is $0 not +$25. and it is not better to gain $100 than lose $50 when you already have $100.

50% loss is exactly equal to 100% gain because if you lose that bet. now you need 100% gain yo get back to the origianl $100. ev to switch is 0, and the advantge in edge to switch is also zero. from that perspective of of a card counter we dont tend to like risking money without an edge so we should never switch.

[Three]

no this is wrong the ev of switching is $0 not +$25. and it is not better to gain $100 than lose $50 when you already have $100.

50% loss is exactly equal to 100% gain because if you lose that bet. now you need 100% gain yo get back to the origianl $100. ev to switch is 0, and the advantge in edge to switch is also zero. from that perspective of of a card counter we dont tend to like risking money without an edge so we should never switch.

Look at it this way. You have $100 then you face the question, Would you risk $50 of it to be paid $100 more pure profit on a 50%-50% bet. That is you bet a 1:1 bet and get paid 2:1.