Ok, I'm going to have another crack at explaining betting/laying and how the calculators work to give you a profit. We'll use very easy numbers to illustrate.
A bookie offers odds of 2/1 for heads to win a coin toss. You put £5 forward to back this result. The bookie puts aside £10, because if you win, you will get your £5 back plus £10 from the bookie.
You have placed a stake and the bookie has put aside their liability to cover the stake they accepted from you
If you win, the bookie gives you £15, and is £10 out of pocket.
If you lose, the bookie takes your £5 stake and you are £5 out of pocket.
You can ensure that you don't end up out of pocket by making the very same bet with someone else, but this time acting as the bookie. You go to the exchange and find someone willing to stake £5 of their money at odds of 2/1, with you covering the payout should they win. This is called laying the bet. It is what the bookie did with your back bet and what you are doing with someone else's back bet. Your liability for this lay is £10, which you have to hand over to the other party if their back bet wins, along with their original stake. If they lose their back bet, you, as the bookie, take their stake.
So you have a matched bet. Whatever side the coin lands on, you will come out even, with no net gain or loss of cash. You will either: win £10 from the bookie/lose £10 at the exchange -or- lose £5 at the bookie/win £5 at the exchange. Zero sum.
Now the bookie tells you that you can have a free £5 bet on a second coin toss, same odds of 2/1. This time round, you don't put forward a stake at the bookie because it's virtual money. The bookie still has to set aside their liability of £10, to pay to you should your back bet win.
You go to the exchange to lay the bet. If you lay against a £5 stake at odds of 2/1, you put forward your liability of £10 against the £5 back bet of someone else.
Toss the coin. You will either: win at the bookies/lose your liability (profit £0) -or- win at the exchange (profit £5). This is not an equal outcome so not a good matched bet.
Can anyone see approx. what value stake you'd have to lay against at the exchange to ensure that you make the same amount of profit, no matter what happens?
Use the formula 'win at bookies - loss of liability = stake won at exchange'.
Hopefully, it will be obvious, with some mental maths, that you need to lay against a stake of £3.33. This will create a liability value for you of £6.66.
Win at the bookies - loss of liability = £10 - £6.66 = £3.34 profit
Win stake at exchange = £3.33 profit.
These two bets are matches. In the absence of such convenient odds to allow us to do this in our heads, the calculator tells you what the exact stake value you need to lay against to make the match.