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I wanted to know how many penhold grip types are there

Three types
1. TPG (Traditional Penhold Grip) or just TPH(Traditional PenHold) :- This is the older style of play using penhold grip where the player uses only one side of the racket on both forehand & backhand. Ther is rubber only on one side of the racket & other side has a paint sheet.
2. RPG (Reverse Penhold Grip) or just RPH(Reverse PenHold) :- This is the newer style of play using penhold grip where the player uses both sides of the racket just like a shakehand player. There is rubber on both sides of the racket
3. HPG (Hybrid Penhold Grip) or just HPH(Hybrid PenHold) :- This is the newer style of play using penhold grip where the player uses both sides of the racket just like a shakehand player. There is rubber on both sides of the racket & the player uses both TPH & RPH strokes

TPG :- Lot of former world champions used TPH using short pips out (with sponge). Some used spinny inverted rubber.
HPG :- First player & probably the only world champion who used hybrid penhold was Liu Guo Liang. He had short pips on forehand and used both TPH & RPH with it . he also used a spinny inverted rubber on his backhand to loop. This is probably the best style of penhold.

RPG :- These players mostly use spinny inverted on both sides of the racket & loop from both sides. They do not play TPH on their backhand side using forehand rubber. Xu Xin & Wang Hao are the best examples.

There is also another older method of classifying penhold grip types before the arrival of HPG & RPG
All grips were essentially TPG
But this classification is still used but it is more about the shape of the racket & how it is held in one's hand rather than the playing method used as in TPG, RPG & HPG

Japanese Penhold (or jPen) & Korean Penhold (or kPen) :- lPen & jPen are quiet similar & the notation kPen is rarely used. This is mostly because Chinese arrived on the TT scene as successful in 1959 and Japanese followed in 60s. Korean successes came in the 80s and after.
Most jPen (or kPen) rackets are rectangular in shape

Chinese Penhold (or cPen) : Most cPen rackets are oval or circular in shape.