Some of my colleagues are insisting me to join a group of 10 colleagues (namely, A, B, C,..., J) in a money rotation game. Each member has to deposit Rs 10,000 per month into a money pool. Amount deposited in the pool for each month will be Rs 1,00,000 and this amount will be credited to the account of one of the members based on lottery. Suppose, A wins the lottery for the first month then Rs 1,00,000 will be deposited to the account of A. The candidate A will not participate in lottery for the next 9 months but he will continue contributing to the pool. And so on. I have no idea as how to invest this amount so that we could get the maximum benefits out of this game. On other hand if I don't participate in this game and deposit Rs 1,00,000 in FD for one year, I will earn an interest of Rs 6,500. What is the maximum possible profit I can get from money rotation game?
There is a big risk:
The other participants might stop once they win, thus if you don't win early the game might stop before you win a month. If it goes six months without you winning and then then stops you have spent 60,000.
There can be legal issues if it is viewed in your jurisdiction as gambling, and that form of gambling is illegal. It might even involve money laundering. Making large cash deposits in some countries can be problematic and trigger additional scrutiny.
There can be tax issues.
Even ignoring all of this, the best way to maximize the return is to win early and hope that others lose interest before you have contributed as much as you have won. If the games goes to completion then those that won early make more interest than they would have with a lump sum, those that win late make less money, but as a whole it evens out.
You appear to be describing a rotating savings and credit association (ROSCA) (references: Wikipedia, Investopedia). These are not usually set up as a "game", but as an informal financial institution that acts as an alternative to banks (ask your colleagues to ascertain this). In effect, the winner of the lottery is given a loan (not a lottery prize or free money).
ROSCAs are useful in communities that have limited access to banking services (e.g. remote areas, places with underdeveloped banking systems, etc.). These associations are based on social trust. Note that lotteries are not a necessary feature of these associations. The recipient of funds could be chosen using a circular queue, or based on submitting a loan application, or using a lottery, etc.
Is money rotation a profitable game?
i.e. How much money can I earn from my "deposits" in a ROSCA?
First, let's prioritize the preservation of capital instead of the potential for profit. ROSCAs are based on social trust among the association's members. If you don't trust the other members, then don't join. If you intend to scam the other members by deliberately stopping your contributions once you get your "loan", then please don't join. If you have access to reliable banking services, then putting your deposits in the bank may be a much safer choice.
If you want to get higher interest on your deposits, you will need to evaluate the situation of ROSCAs vs banks. This is highly dependent on the rules and members of the ROSCA in question. You will need to balance the risk of loss of principal (presumably higher in ROSCAs) vs the interest rates offered. There's no point in accepting a minuscule increase in the rate of return if the risk of loss of principal becomes unacceptably high.
On other hand if I don't participate in this game and deposit Rs 1,00,000 in FD for one year, I will earn an interest of Rs 6,500. What is the maximum possible profit I can get from money rotation game?
For the ROSCA described in your question, if you play fairly, the maximum profit is zero because no interest is paid. Since you are looking for profits, you will be better off with the FD.