Couldn’t find any information on this, and it seems pretty important for properly planning your crucible runs. Here’s a table for Gladiator difficulty - other difficulties can be found in this spreadsheet.
Legend
Tier rewards: tributes earned for finishing every 10 waves
[ul][li]New: tributes earned in the first run[/li]
[li]Restart: restarting a run after finishing/dying[/ul][/li]Finish rewards: tributes earned when electing to end the run
[ul][li]New: starting a run from wave 1[/li]
[li]Restart: restarting a run after finishing/dying[/li]
[li]C 50: starting a run from wave 51[/li]
[li]C 100: starting a run from wave 101[/li]
[li]C 150: starting a run from wave 151[/li]
[li]Fail: compensation for dying[/li]
[li]C Fail: compensation for dying if starting from a checkpoint[/ul][/li]
Tribute costs
[ul][li]Towers/banners: 5 to build, 8 and 12 to upgrade (25 total), lasts until full reset (resets that cost tributes do not remove buildings)[/li]
[li]Buffs: 12 each (48 total), lasts 25 minutes[/li]
[li]Starting from checkpoint: 8/15/25 to start from 51/101/151, respectively[/li]
[li]Soft reset: 5/15/30 for first, second and third time, respectively[/li]
[/ul]