[jogsxyz]

[ QUOTE ]
Playing heads up limit hold em - how many bets max can it be optimal to go without the nuts on the river?

[/ QUOTE ]

There's no one size fits all answer. It depends on the board on the river.
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You: KsQs
Board: QdJs8s, 4c, 2s

You would be willing to maybe put in the 2nd or 3rd raise.
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You: AhKs
Board: KdJs8s, 4s, 2s

Doubt that this hand is worth any raises.
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You: AhJs
Board: QsJdJc, 4d, Qh

Opponent bets into you after being passive. This
is a crying call.