Its not that simple. The average utilisation of a game might be 250% but that is an average over a long period of time. You can achieve that on a 4 core machine with 400% utilisation and the CPU doing nothing for 37.5% of the rest of the time. With 6 cores you would have the core idle for 58%. Every frame of a game for moments is always bottlenecked by both the CPU and the GPU. No game is 100% one way, it just doesn't work like that at all.
The 6 core CPUs on sandy bridge are actually sometimes noticeably faster than a 3770k in games and rarely falls behind because the 3930k is just 200Mhz slower than the 2600k. For example this review:
http://gamegpu.ru/action-/-fps-/-tps/battlefield-3-aftermath-test-gpu.html
Admittedly in Russian but shows a 20% lead to the 3930k over the 2600k with a 690 at 1080p ultra quality. The same site shows the Star Craft 2 heart of the swarm also gives a slight boost for the 3930k such that it rivals the 2600k despite being slower clock speed. Far cry 3 is another example of a game that uses those cores and gets a few percentage points of additional minimum and average FPS. None of these games peg the CPU to 100%, but they do show that lower utilisation on average doesn't actually equal no need for great than 2.5 cores.
Be careful about equating averages to actual performance measurements, it isn't that simple. Only parts of games can run in mass parallel but that can make a noticeable difference in performance. The 3930k is a better gaming CPU than the 3770k in some circumstances, and sometimes its worse because of its IPC reduction. But its also interesting to look at the frame time graphs they produce, 6 core SB-E's tend to have less long jitters especially with hard drive loading, because they have spare core performance to put to the task.
I am not suggesting you swap in a 3770k for a 3930k, but I am seeing its not as simple as the calculation you have done to determine how many cores you need. Only testing will show the benefit or not of more or less cores.
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