I can't speak about gaming but for more general contracting the multiplier is 1.75 - 2.5x of a normal employee's salary
There are a lot of reasons why employers hire contractors, some more valid than others.
In my limited experience, it's rarely worth it, mostly because the relevant processes are never in place to ensure that loads of knowledge doesn't walk away with the contractor at the end of the contract
Off the top of my head I know that contractors don't get benefits such as holidays, pensions and other employee benefits.
Their contracts have an expiration so they're easier to get rid of on short notice.
Also they are treated as capital expenditure versus operational expenditure. And I believe that you can do some accounting that is beneficial tax wise to a company.
One that isn't mentioned much is avoiding corporate overhead costs, which I found interesting when I learned about it.
Basically some big companies charge their divisions fees for upkeep of facilities, paying the finance team salaries, etc based on the number of employees in the division.
So if you can have ten employees you are only on the hook for $1M/year in corp fees even though you actually have three "consultants" sharing desks with every employee for years-at-a-time. If you added the consultants to the employee roles then you would become a 50 person division, owing $5M/year to the home office.
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The CAPEX vs OPEX thing is a big driver too, of course, but there are definitely ways to classify employees, at least partially, as capex.
It's why you can make an exempt employee fill out a timesheet to charge back projects which you have put into the capex group.
A few jobs ago my group was told to find 80% capex or find new jobs. Most fridays were spent negotiating with project managers in tasks-for-hours swaps.
Some of the above are perceived by PHBs types as there is always a finite pool of people with the skillset that is needed for the job at the skill level required etc...
There are a lot of reasons why employers hire contractors, some more valid than others.
In my limited experience, it's rarely worth it, mostly because the relevant processes are never in place to ensure that loads of knowledge doesn't walk away with the contractor at the end of the contract
edit:
Should clarify that I'm in the UK.