Disclaimer:
I am only a mere low to mid masters player jumping between 4300 to 4500 mmr. Everyone has their own way of playing; I am simply writing out my views on this matchup which are based off of my hours of viewing of top level streams, such as those of Maru/Clem/Cure. The pros I watch and copy are Maru Future, Clem, Cure, and many other high grandmaster “small” streamers. This write up could be regarded as incorrect by many people like I said, I am a low-mid level player.
Opener:
Either 16 16 Reaper Fast Expand or 15 16 Gas First Reaper Expand and then make a reactor on rax.
The 1-1-1 phase is very important part of TvP. It is much more flexible than in other matchups. You can react or decide the tempo. You can do 1-1-1 pushes with marine tank banshee or play super safe with tank raven; you can play very harass oriented style with hellions + banshee or double minedrops. There are many variations unlike TvZ where you go hellions every game or TvT where you always do marine raven.
Harass Variations:
1st Case (Reactor Hellions with/without Banshee:
Swap rax with factory and reactor out hellions from the factory while making techlab with rax (optional) to swap with starport for banshees.
I usually do this when I scout and see 2 pylons in main + standard nexus expand meaning they did not place their 20-21 pylon in nat (incredibly rare), so they did not wall off the nat; I can punish this by reactoring out hellions and playing yolo with first 2-6 hellions and following it up with banshees; think 1-2 punch combo. I also do this when I see protoss being incredibly greedy with 3:30 3rd nexus. You can still pull off reactor hellions vs wall offs if you make a medivac rather than banshees and transition to 3cc faster; however, I prefer doing 3 hellions of naked factory if I were doing medivac hellion drops.
2nd Case (3 hellion or mine drop):
Make hellions/mines off the naked factory and a medivac as soon as starport is finished. Note: you can proxy the factory and starport if you play off 1 base.
Three hellions is a magic number for one shotting probes even with the battery if all attack at same time. This probably has the fastest transition to 3-1-1 assuming all production are not proxied. If I were to go 3cc off this I would go for 2nd medivac + hellions/mines. There are variations where you get an armory for cloaked mines with 2+ medivac drops.
Safe Variations:
I usually do this kind of variations when I scout something from protoss like warp prism attack or blink all ins. I mostly transition to 3cc off the safe styles because the transitions for 3-1-1 are usually too late for the timings to do anything. Some of these openers can be used for 1-1-1 pushes.
1st Case (2 Tank Raven):
Pump out marines, make a techlab on factory then swap with starport for raven and the factory makes another techlab to make tanks.
This is one of the safest variation, it shuts down DTs and blink all ins. I usually do this when I see twilight first. You can go 3cc off this and keep making tanks or 3-1-1 and make mines or a 3rd tank to push at 7 mins with +1 upgrade stim cs.
2nd Case (Cyclone Viking):
Pump out marines, 1-2 cyclones and 1-2 vikings.
One of the best anti warp prism aggression setups. Also works incredibly well vs stargate. Note for stargate: you can make a tank instead of 2nd cyclone and do a 1-1-1 push vs stargate. You can decide how much you want to commit with this push. Commitment levels may very from semi aggressive (fake pushes to force batteries and protoss isn't playing that greedy) or committed pushes with pulling 4 scvs to make bunkers at protoss 3rd if they are being very greedy with 4 minute 3rds. These kind of pushes are very weak vs blink openers so I only recommend doing this vs stargate openers.
Aggressive/All ins:
With these kind of variations, you can pull the bois (optional) and cut scvs for constant rallies.
Marine Tank Banshee:
Pump out marines, factory makes techlab then swaps with starport for banshees and makes its own techlab to make constant tanks.
This is a classic build. Done by INnovation many times. You usually want to pull scvs with this for bunkers and hard contain protoss nats. I prefer doing with on maps without ramps right in front of the nat. I usually go 3cc off this to get my eco back into shape after the push ends.
[u]Special Variation (1 Base All in):[u]
wall off at 18 supply (16 16 expand) then get reactor after marine + start factory and 2nd rax then techlab on factory, starport, and spam marines. Make 2 tanks + medivac and pickup the tanks and moveout.
Just another fun 1 base 2-1-1 all in.
Transitions:
Now you have two choices, 3-1-1 with single engy bay or 3cc 3-1-1 with double engy bay. Note that in order to transition to standard play in TvP, you need double techlabs + 1 reactor which are usually made after certain units (mine drops or hellions) are made or already made in order to make tanks, ravens, banshees.
First Case (3-1-1):
Make 2 raxes around 3:30-4:00 (depends on $$ and 1-1-1 variation) next to the techlabs and lift starport and factory to make 2 reactors for biomine push or reactor (medivacs) tech for a biotank push.
If you do 3-1-1, you can do a timing that hits at 6:30-7:00 with +1 attack, cs, stim. I prefer this with 1-1-1 variations where you don't really make more than 1 set of units, for example just one mine drop off naked factory into 3-1-1 or 1 raven into 3-1-1.
Second Case(3cc):
If you transition to 3cc, you want to plop down 3rd CC around 4:00-4:40 (assuming 1-1-1 harass or safe variations) and then make 2 raxs at 4:30-4:50 with double engy bay.
With 3cc, you can go for a 1-1 timing around 8 minutes with 130-170 supply. This timing can vary in either biotank or bio viking ghost. This will be discussed later. If you're doing committed 1-1-1 harass or pushes, your 3cc is going to come down much later around 5+ minutes.
Followups:
3-1-1:
With 3-1-1, you can followup with 3rd CC at 6:30 then go up to 5 rax or extra 2 raxs at 4:50-5:20 for 2 base all in. With 3rd CC option, usually you would be macroing and saturating the 3rd mineral line while microing your +1 timing. After the timing, you can either followup with 3 base all in with +1 armor where you do not get 3rd gasses at all, and get 3-5 ghosts with vikings since you have gas from not getting armory and 2-2 upgrades.
3CC:
You go up to 5 rax. Now you have 3 mainstream options:
Option 1: You can cut scvs and not bother taking gasses at 3rd, and don't get armory + 2-2 for maxed out 1-1 3 base all in.
Option 2: You can go for 1-1 timing with/without ghost viking or depending if you delay the gasses at 3rd, armory and 2-2 upgrades or not. You also can go for lib timings where you make 2-6 libs and push with the upgrades. Do not get range as you won't have enough gas. This option could be borderline all in if you cut scvs at 55-60 but you can still macro out of it assuming you take a 4th.
Option 3: You can go for normal gas timings, full out macro for lategame. Normally I would play defensive and get 2-2 ASAP then spend all my gas on tech units such as ghosts. I mostly go for 5-1-2 setup with slightly faster 8-9 minute 4th than the previous options mentioned and play for the ghost viking 2-2 maxout timing into ghost viking lib lategame. I have seen some people go for 3 factory mass tank turtle lategames. Some do 5-2-1. Some do full on bio-mech switches. This is usually freestyle and ties heavily into your stylistic preference. Some people like playing mass bio multiprongs off normal 3cc eco into fast 4th CC ghost viking.
Closing Notes:
This is my interpretation of the TvP standard matchup. Let me know about your own interpretations or thoughts! Thanks for reading!