I suspect that the chances of a 3rd party winning are orders of magnitude lower than a 1st or 2nd, so the expected value from you having the deciding vote would be too small. But in terms of policy influence, if the 3rd party does unusually well (without winning), I agree that can be significant. Indeed I recall an example of this happening in the UK in the 1990s, when in one national election the Green party (then the 4th or 5th party) did unexpectedly well, albeit still only getting a few % of the vote, which immediately made the major parties start saying how important the environment was and announcing new policies.
I suspect that the chances of a 3rd party winning are orders of magnitude lower than a 1st or 2nd, so the expected value from you having the deciding vote would be too small. But in terms of policy influence, if the 3rd party does unusually well (without winning), I agree that can be significant. Indeed I recall an example of this happening in the UK in the 1990s, when in one national election the Green party (then the 4th or 5th party) did unexpectedly well, albeit still only getting a few % of the vote, which immediately made the major parties start saying how important the environment was and announcing new policies.