25nl: is this a dumb river bet?

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You bet $6 into a $10 pot on the river. Let's go through some math:

Pretend you have a machine that flips a coin. The coin toss costs you $10 and if you win it gives you $10 (plus your money back). If you lose it just takes your $10.

This would be a useless game because in the end you'd end up with the same amount. Half the time you are earning $10 and half the time you are losing $10.

Now imagine the machine charges you only $5 per turn. On the first turn you pay the $5 and win it. You are now $10 richer. On the next turn the machine wins so you lose your $5 entry fee.

If it goes win, lose, win, lose, win etc. then you will be earning $10 for each win, and losing $5 for each loss. So to make it fair the machine would need a special coin that lets him win 2/3 of the time.

For this hand, you are betting about $5 to win $10. The guy needs to fold only 1/3 of the time for you to be ahead. So take into account these facts that might make him fold:

- You bet hard preflop, flop, turn and river

- He check / called the whole way with a flush on the board (and two straight draws: AK and 45)

- He was in the BB so might be defending with something other than Ax / Kx

So he could have QJ / two diamonds / JT which he will definitely fold for $6. He could also have Kx / underpair / 5x which he might fold for $6.

If he has Ax he is definitely not folding because he will split against any other ace. 4x will also not fold obviously.

So it is actually a good bet on the river because he'll fold more than 1/3 of the time IMO.