Pon and Chi (1)
Are you consciously aware of the difference between these two kinds of calls?
Pon Is Four-Times Speed, Chi Is Two-Times Speed
You can pon from any of the other three players, but you can chi only from the player to your left.
In other words, pon is easier to make than chi.
Example 1
Pon 
In a shape like this,
discarding either or leaves the same one-shanten shape with four types and fifteen tiles of acceptance.
But a chi on 
can only come from the upper player,
while and can be pon'ed from anyone.
So even though both are “four-tile” acceptance,
the first is worth only eight tiles' worth of speed, while the second is worth sixteen.
Therefore, the standard discard is .
If You Are Only Cancelling Ippatsu, Use Chi
When you call only to cancel an opponent's ippatsu after riichi, the standard move is to use chi.
If you pon to cancel ippatsu, you lose two genbutsu against the riichi player.
Even if you cancel ippatsu, if you then deal in yourself, there was no point in calling.
Whether you use chi or pon to cancel ippatsu,
you should do it only when you are confident you can still fold safely afterward.
Theory Summary
Using pon to cancel ippatsu is high-risk.
If you are calling only for ippatsu-cancel, chi is the safer choice.
3. Pon or Chi?
Sometimes a tile discarded by the upper player can be taken either by pon or by chi.
In those spots, there are cases where pon is better and cases where chi is better.
Example 2
Dora 
Discarded
With Example 2, if it is still early in the hand, you could pass and hope for a good-shape improvement in the pinzu block.
But from the middle game onward, you would usually take the call and go to tenpai.
So then, should it be pon or chi?
Kan is obviously out of the question.
Here, pon is better. The reason is what happens if you later draw the dora.
If you pon
Pon 
If you chi
Chi
If you pon, you can later swap with .
If the situation allows it, you may even add a kan.
Pon Draw
Now let us look at a honitsu hand where the tile discarded by the upper player can be taken by either pon or chi.
Example 3
Discarded
The conclusion first: here, chi is better.
If you pon
Acceptance: 3 types, 9 tiles
If you chi
Acceptance: 3 types, 7 tiles
If you look only at the raw acceptance count, pon seems better.
But remember the earlier rule:
pon is four-times speed, chi is two-times speed.
When you think in terms of speed to tenpai, a shanpon acceptance that can be pon'ed is worth a multiple of its tile count.
If you account for that:
If you pon
(2pt) + (8pt) + 
(8pt) = 18pt
If you chi
(4pt) + (8pt) + (8pt) = 20pt
That reverses the result.
The chi shape, even though it has fewer raw acceptance tiles, actually wins in speed to tenpai.
And in terms of value, the chi line also keeps the extra one han from yakuhai ,
so here chi is overwhelmingly better.
Theory Summary
Acceptance that can be taken by chi is worth twice the value of a menzen-only acceptance.
Acceptance that can be taken by pon is worth four times the value of a menzen-only acceptance.
Original Japanese page: http://beginners.biz/naki/naki03.html