Ps3 to ps3 and then to xbox

is it posssible to get a ps3 arcade stick and then use a ps3 to ps2 converter and then use a ps2 to xbox converter so i can use it with my xbox.

normally if one had an xbox, one would get a ps2 stick and just buy a ps2 to xbox adapter but ps2 sticks are exspensive right now but i see some hori sticks on ebay for cheap but it is for ps3

First, there is already an adapter/converter thread.

Second, there is no such thing as a PS3 to PS2 converter.

Third, chaining two adapters would cause a lot of lag.

If you get a PS3 stick your best bet would be to change out the PCB for a PS1 PCB.