[Tee]

Okay - with the entry fee being non-refundable, the Expected Value (EV) of each play is:

EV = 0.25(-4) + 0.25(-3) + 0.25(2) + 0.25(4) = -0.25

Thus you would lose (on average) 25c every time you played.

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If the "loss" and "gain" were relative to your initial state, prior to paying the entry fee, then the EV would have been as follows:

EV = 0.25(-3) + 0.25(-2) + 0.25(3) + 0.25(5) = 0.75

In this case you would win (on average) 75c every time you played. Sign me up for a few million rounds of this game please

[cgfirecoral]

Another way to think of this mathematically is this:

Pay $4 to play.
You can now win $0, $1, $6, $8.

On average, you're still going to win $15 for each $16 wagered - still a losing proposition.