how many number of moves ahead can an average player think ?

Indeed.

It varies greatly by position. In some endgames, 20-30 moves is easy. In most middlegames, four or five moves would be impressive. I can remember a few instances in OTB play where I calculated precisely the critical lines eight or nine moves deep.

Here is one example from my last OTB event:

My deep calculation begins with this position.

16...e5! is best. It makes sense positionally, but I had to verify that it was correct tactically.

I had spent some time preparing this move. This moment appeared the correct time to make it. If not now, White might play Ne5, which would then necessitate more preparation.

Calculation was simple and straight-forward if White replied 17.Nxe5 or if he replied 17.dxe5.

However, the zwischenzug 17.Bb5 creates complications. It was this line that I analyzed for thirteen minutes.

I briefly considered a) 17...Bd7, and spent a few minutes looking at b) 17...e4. I considered the latter as an unattractive, but safe option. Here, my analysis concluded in a position where I thought that I was better, but Stockfish evaluates as equal. However, I missed the best move half-way through this line.

The line that took the longest to calculate and assess begins with c) 17...exd4! It is the best move.

a) 17...Bd7 is Stockfish 4's second choice. I gave it only cursory examination, but realized that some of the ideas in the lines I did examine would be present.

b) 17...e4 is Stockfish 4's third choice.
I looked at 18.Ne5 Bxe5
     Unexamined was the correct 18...Ne5! 19.Bxe8 Nd3-+.
My analysis continued 19.dxe5 Rxe5

I assessed this position as better for Black. Black is two pawns ahead, but Stockfish sees the position as equal. Black can generate threats against h2, but White has sufficient defensive resources. Black's pawn center is fragile, and thus his material advantage is temporary.

My analysis did not extend to 20.c4, which is White's only move. Otherwise, Black has secured an advantage with subpar moves.

c) 17...exd4 occupied the longest portion of my thirteen minute think. It is the best move.

I did not look at 18.Qd1, 18.Qf1, nor 18.Qd3. 18.Qxe8 struck me as the critical line, as it is a direct effort to refute my idea. Black's back rank has weaknesses. These are not fatal, but White has several forcing moves. Moreover, there are some material imbalances to consider.

18...Nxe8 19.Rxe8+ Bf8 and now more branching occurs.

Examining branching in one of several possible lines four moves from the current position has not been the norm in my over the board play. It must become so. In correspondence chess, such analysis is easier to perform thanks to such tools as analysis boards, database software for recording and observing possible positions, and the old fashioned paper and pencil with a physical board. Doing this analysis under tournament conditions with the clock running while looking at a static board requires imagination. I closed my eyes several times in order to imagine the board.

c1) Bxc6 Qxc6 21.Ba3 (the computer prefers 1.Ne5, which I do not recall considering) 21...Bb7 22.Rxa8 Bxa8 23.Nxd4 Qxc3

Black's advantage is clear, but I thought that White had a more dangerous line.

c2) 20.cxd4 seemed less dangerous, and I did not go deeper.

c3) 20.Nxd4 seemed critical. Stockfish vacillates between this move and 20.cxd4 as best for White.

20...Bb7 (I do not recall looking at 20...Nxd4, which the engine considers best) 21.Rxa8 Bxa8 22.Nxc6 (Stockfish prefers 22.N2f3) 22...Bxc6 23.Bxc6 (23.Bd3 may be better) 23...Qxc6 24.Rxa7.

Although I was not certain my advantage was overwhelming in this position, I thought that I would probably choose this line. I knew that I could spend more time examining it after playing 16...e5. 

Depends on the position, but by the time I hit 1600 USCF (pretty average) I could play an entire game of blindfold

Good moves or random moves?

I can think three ahead. At least. I'm an average player.

I can "see" (for my turns) 2-3 moves ahead... but often by move 2 or 3 into my plan the opponent derails it, or at the least forces me to modify it. Murphy's Law: No battle plan survives first contact with the enemy.

As folks noted, it depends on the position and whether the moves are forced.  I'm probably a below average player, but I have calculated positions out 10 to 15 moves ahead -- that's not to say that my calculations are always accurate or I never make a mistake.  I will typically calculate what I think is the probable line of play (i.e., optimal move for each player) out 5-10 moves, and I will check alternative lines out to 2-3 moves or until I think one or the other player has gained a significant advantage in that line.  This does tend to make me susceptible to clever sacrifices.  For example, if I calculate a line leading to a fork that allows me to go up a piece, I generally assume that the other player will not play that line as it gives me an advantage.  However, by not looking past the fork, I might miss some follow-up moves by my opponent that give him a strong attack.  Similarly, I might miss the opportunity to make a great sacrifice by not looking past what I perceive to be a mistake.

Andy Soltis has claimed that to be a "strong" player, one only needs to be able to calculate 2.5 moves ahead.

1899, but it was 1929 when I did all that thinking (I gave up a 500 point upset in the first round of the event).

Umm, 5? (10-ply)

Just my guess. 

lol :-)

am sure we all have gamss like that at times

When I asked an IM this question he told me that most of the time he looks 3 moves ahead. His advantage is that he can tell quickly what the position is like at that time. Most of us patzers cannot assess a position 3 moves ahead. 

Average on this site? Less than one.

to be realistic with this question, the situation on the board is what a player should assess, rather ghan try to assume his opponent's moves.

I think in terms of moves behind

It depends at what you think is an average player.

I cannot play blindfold and I don't think I'll ever be able to. It's the type of skill that one either has or does not have.

For me...Id say on average 2-3 moves.  if its a forcing line then its deeper that that.  A lot depends on the position, how much effort i feel like putting in, and if i just ate.

I can play blindfolded a long game, so I probably can calculate 10 moves forward correctly atleast from a given position. (complex middlegames) usually do I not calculate, but when I do it is not that many moves, maybe 2-6 moves.