An improved understanding of guarantees

Last night's tournament gave me the information I needed to improve my understanding of guarantees. It turns out some of my previous assertions about them were just plain wrong. Here's what I now understand:

1. I have joined guarantees before

2. Guarantees, like all tournaments, have an entry fee

3. PokerStars doesn't advertise what the entry fees are for guarantees; they simply advertise what they call the buy in; however, this amount is really the sum of the actual buy in and the hidden entry fee

4. PokerStars provides you with the information you need to calculate what the entry fee for the tournament was, as long as enough players joined the tournament to cover the guarantee; in this case, you can use the following formulas:

actual_buy_in = prize_pool / num_entries

entry_fee = stated_buy_in - actual_buy_in

5.There's no foolproof way to calculate the entry fee if not enough players joined the tournament to cover the guarantee. However, that's a rare event, and the easiest thing to do in this case is simply to declare that the actual buy in is the same as the stated buy in, which makes the entry fee zero.

style flavor buy_in  entry players entries paid place winnings

MTT-B NLHE   880000 120000       9     300   55    91        0

delta: $-1,000,000
MTT with bounties NLHE balance: $-5,407,820
2022 balance: $-2,261,000
blue distance: $2,278,200
balance: $92,582,953