If Dr Strange knew the outcome why did he put up the fight?

He watches several million outcomes and determines that only one path to victory exists.

Presumably he will have seen the exact sequence of events that need to occur for things to work out in their favour, which will likely have included the fight with Thanos itself.

It may become clearer in the sequel how things work themselves out, but possibly the way Strange held onto and then gave up the stone will prove in some way key to the final resolution (perhaps even just that Tony Stark is needed to win the day in the end)

Edit after Endgame release:

Tony Stark was indeed absolutely key to the one in 14,000,605 possible futures viewed by Dr Strange, for a few reasons:

1. Tony was the only person who could have figured out the "time travel GPS" device
2. Tony was the one who realised that they could gain more Pym Particles and the Tesseract by jumping to 1970 after the problems collecting it in 2012
3. Tony designed and built the new gauntlet using his nanotech
4. Tony was the one who performed the final snap to destroy Thanos and his army

It might be explained in the sequel of this movie, but till then there is a simple explanation.

As you mentioned that he wanted to save Iron Man, it is possible that Dr. Strange gave the Time Stone to Thanos to spare Tony's life because he saw something important. If we go a bit behind in the movie, we saw that Dr. Strange saw a millions futures and there was only one which they could win in.

Though we don't know what exactly Dr. Strange saw in those future, it's possible that he saw something, something important, related to Iron Man, which could give them a chance to fight again and help them win the battle against Thanos.

Update: and in the Endgame, as mentioned in my other answer,

He must have seen that Tony will be the one who will invent the time travel formula and build a second Infinity Gauntlet (of course with help of Professor Hulk) and will then snap Thanos and his army in Endgame.

Even when Iron Man asks Strange if this is the future where they win, Dr. Strange says,

If I tell you what happens, it won't happen.

They have to keep the fight going as per that win future Strange saw.

Doctor Strange's actions indicate two priorities, based on his analysis of possible futures

STRANGE : I went forward in time... to view alternate futures. To see all the possible outcomes of the coming conflict.

QUILL : How many did you see?

STRANGE : Fourteen million six hundred and five.

STARK : How many did we win?

STRANGE : ...One.

Priority One: Save Tony Stark

STRANGE: [to STARK] If it comes to saving you, or the kid, or the Time Stone, I will not hesitate to let either of you die.

However, Doctor Strange completely reverses this after his analysis of possible futures and the subsequent battle with Thanos.

STRANGE: [to THANOS] Spare his life and I will give you the Stone.

Priority Two: Surrender the stone to Thanos, without giving any clue that he intends this all along

THANOS: [to STRANGE] You’re full of tricks wizard. But you never once used your greatest weapon...

There are a number of analyses on the Internet that back up this summary:

• Why Doctor Strange Definitely Needed To Make That Terrible Trade In Avengers: Infinity War from CinemaBlend
• If Doctor Strange's goal was to get Thanos to let his guard down, he succeeded from ScreenRant
• The secret plans of Doctor Strange from Forbes
• etc.

I agree with AJs answer, though I also wanted to add that Strange's plan may have been as simple as delaying Thanos for a certain length of time, giving the people back on Earth time to get into the right places. He held back Thanos as long as he could, and only then gave Thanos the Stone. Again, it's probably going to be unclear what the plan is until Avengers 4

I might be wrong here but I think it all goes back to the past:

All those who were killed by the gauntlet where not in the Avengers' 2012 New York battlefield. The remaining heroes (Thor, Iron Man, Captain America, Black Widow, Hulk) are still alive and Hawkeye is yet to be seen. There is no way he will he left behind. Nick Fury at that time was on the battleship not on the battlefield, and as for Loki, he was not killed by the curse of gauntlet but by the hands of Thanos.

Additionally, Dr. Strange would have given up the time stone for something he saw in time, likely involving Iron Man and co.

Checkout the Stark technology, B.A.R.F

Tony Stark used B.A.R.F to revisit the memory of seeing his parents Howard and Maria alive for the last time so it might be used to senD some sort of signal to avengers in the past or something. The main plot is that the Avengers can use B.AR.F. to play with the time. Additionally, there are some leaked photos of Avengers 4 that show

heroes wearing old costumes.

The battle and its outcome--Strange giving the stone to Thanos, and perhaps even the dejection that Tony feels--are a prerequisite for the Avengers' eventual victory in the future seen by Strange.

While thinking about this I also came up with the following life guideline: Don't ask why the man who sees the future does what he does; you'll find out soon enough.

There is one additional possibility on the other fork of this decision tree.

Strange may have seen the successful outcome, and may have realized that they have failed. For example, maybe the outcome depended on Starlord keeping his temper in check. Since Strange now knows that they have failed, and that Thanos will succeed, he may be acting to simply maximize the number of heroes who survive the fight, as the remaining half of the Earth's population will still need heroes.