### Comment:
Shouldn't the lose be $-6k?

### REPLY:
no.  if you lose 10k,  you will have 10k less.   
  
 you are probably thinking  that the loss is 6k relative to the taxes? You can calculate in this frame, but then you have 
  
 do nothing = 0. 
  
 lose = -6k 
  
 win = +10k - 4k (tax on the winnings) = 6k.  
  
 EV= 0.5\*-6k  + 0.5\*6k = 0.  
  
 nothing changes.    EV is still the same as when doing nothing.

### END.