EV and Hedging

Yo guys,
you finds your self in the following situation:
- Event: 4 playesrs competition. only 1 win. (players: A,B,C,D,)
- Position: bought (back) 2 units of player A winning @5 (fractional odds: 4:1).

some thinking:
Why i took this position?
=>Because i think is a +EV position (i.e. i have an edge).
How did arrived to the conclusion that i have an edge?
=> I've assume that there is one mkt that is giving me the efficient price, i.e. the "true" probabilities of this event. i then compare that price with other mkt.
==> the efficient mkt is @3 => therfore i see a miss price here. simply put: i can buy in one mkt @5 (1/5 implied probability) and sell the same thing on another mkt @3 (1/3 implied probability). Here im buying low and selling high (= making money). For the sake of clarity the efficient mkt is an exchange (this is why im saying: you can sell (i.e. lay)).

NOW the question: I found a +EV bet by comparing the (assumed) "true" probabilities of the efficient mkt with another mkt and found a difference between the two. Should i closed the trade and hedge on the efficient mkt and capture all the EV or shall i be naked, not hedge, and run the bet till expiring?

My thinking is the following: since the the true probabilities are given from the efficient mkt, the trade on the efficient mkt is by default a 0EV trade (those are the true probabilities), therefore i shuld hedge and capture all the EV that ive estimated in this bet. Moreover the EV that im estimating is the same if i hedge or not(ofc), the difference is the risk if i hedge ot not. Im reducing my risk (variance of result here) by hedging with a 0EV hedge (i.e. by hedging im assuring to get the EV in all scenarios, actually looks like it will not be an expected value but a sure value => Im gettin a $$ amount equal to the EV in all the 4 scenarios.)

What do you think? I saw a lot of discussion about not heding vs hedging ecc.
Am i doing any logical mistake in my reasoninig? i would love to have a discussion on this.

Cheers,