I know of no browsers that allow the user to select an interface to bind to, although there might be. Most browsers let the operating system decide. The OS then consults the routing table, which you can configure to associate destination IPs with a particular interface. However, it seems like you want to use different interfaces for the same destination, for which the routing table does not suffice.
Third party software may do the trick though. I've found ForceBindIP to be an invaluable networking tool. It does exactly what it says on the tin: forcing programs to bind to a specific interface, allowing control over which source IP to use per process rather than per destination, even when the program itself does not have this feature.
As an example, I tried connecting to a web server 'Neon' using a machine with two IP addresses, 192.168.120.32 and 192.128.120.64. The first time, it used the former by default. Afterwards, I launched the browser using forcebindip.exe 192.168.120.64 firefox.exe
and visited the same page. The access log below confirms both requests originated from different addresses:
192.168.120.32 neon - [10/Feb/2014:14:14:03 +0100] "GET / HTTP/1.1" 200 1568 "-" "Mozilla/5.0 (Windows NT 6.1; WOW64; rv:27.0) Gecko/20100101 Firefox/27.0"
192.168.120.64 neon - [10/Feb/2014:14:15:02 +0100] "GET / HTTP/1.1" 200 1568 "-" "Mozilla/5.0 (Windows NT 6.1; WOW64; rv:27.0) Gecko/20100101 Firefox/27.0"
You don't give us any information. What control do you have over the game? Can you specify the IP it connects to? Does it use TCP? UDP? – David Schwartz – 2014-02-10T13:36:00.093
It is a flash-based game. Either a browser or a stand-alone flash player can be used to play it. The game uses TCP. There are about 30 servers one can connect to by entering the appropriate server name into the browser or flash player. I'm not aware of any other ways of controlling the game. – Yekoor – 2014-02-10T16:26:17.130
Ahh, then you have your answer below. – David Schwartz – 2014-02-10T16:27:11.650