ummm..... no.
We are talking about the bet on the turn... when considering that bet we need to look at the expected value for the individual wager.
At this limit, I don't see him stealing the pot. In other words, the chances of all four players folding is so unlikely, that it will not even be considered in this point. However a bet has a very good chance of knocking out 1, maybe 2 players.
With the first point in mind, at the turn, he is a 4.1:1 underdog to make his flush by the river (assuming no one else is on a flush draw). Therefore, in the best possible circumstances, (that when he bets, no one folds), he is getting 4:1 from the pot on that bet. Therefore, the bet has a slightly negative expectation.
Checking on the turn is correct.
Of course I will close here with the standard poker strategy disclaimer... "It depends on the situation, your opponents, table texture, yada yada yada... "
But the numbers don't lie.
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