Riichi Theory (1)
Here are a few basic principles about riichi.
Immediate Riichi Is the Default
A common beginner pattern is to sit in damaten for several turns, then suddenly declare riichi on a tsumogiri.
Example 1
Dora
This hand may still be one step away from sanshoku, but once you reach tenpai, you should riichi right away.
The only improvements are 
,
so waiting is unfavorable.
There used to be a theory that said, "If the number of improving tiles is greater than the number of winning tiles, stay damaten," but that way of thinking is outdated now.
It hurts too much if an opponent discards 
,
which you still cannot win on yet.
If that is the case, you should not wait even one more turn. Riichi immediately.
Example 2
Draw 
Dora
This one is also an immediate riichi.
Staying damaten, passing on the low-value ron, or "watching the table for a few turns" before riichi are all losing choices.
Saying "I'm waiting for the right ippatsu timing" is nothing but a joke.
The longer you delay riichi, the lower your chance of winning on ippatsu becomes.
Theory
At tenpai, decide whether the hand should be riichi or damaten.
If it should be riichi, declare it immediately.
If it should be damaten, stay damaten unless the situation changes.
2. Use Tsumo as Your Baseline
"A wait like this will never come out..."
This is another kind of negative thinking that beginners often fall into.
Example 3
Dora
Even if the wait crosses the dora,
and even if your own discard row already contains ,
you should still riichi without hesitation.
If it does not come out, then just keep drawing until you tsumo it. Because this is a ryanmen wait, the chance of tsumo is still perfectly real.
Example 4
Dora
This is an even less likely winner: a penchan wait on the dora itself.
Staying damaten to wait for iipeikou is a passive way to play. Even if ron is almost hopeless, tsumo is still possible.
If you get lucky and draw it yourself, it is 1300/2600. That is enough reason to riichi.
Except for tanki waits, you do not need to weigh "how likely this wait is to come out" too heavily when deciding on riichi.
No matter what the wait is, if an opponent is pushing, it can still come out. On the other hand, if opponents are fully folding, even a wait that looked easy from the discards often does not appear.
So instead of trying to guess whether it will be discarded, it is better to think from the baseline of tsumo wins, and to evaluate the hand by the number of winning tiles.
Original Japanese page: http://beginners.biz/reach/reach05.html