4-01 Three tiles away from Upper Four or Lower Four? No problem!
Given the right starting tiles, it can be easy to go for Upper Four, which must be constructed of tiles 6 or above, or Lower Four, which is made with tiles 4 or below. But some International Rules players tend to steer away from these combinations.
For example, take Figure 1. Some players would discard and and go for a Mixed Shifted Chows/All Chows combo. But the superior move is to go directly for Upper Four. You would prefer to be able to meld pungs from any player rather than to be dependent upon melding chows from the player on your left. The hand shown in Figure 1 has plenty of pairs, making it an ideal opportunity to pung aggressively and go for a high-scoring combination.
Either tile completes the hand
Next, consider Figure 2. completes your hand, giving you Upper Four. But completes your hand, as well, giving you Mixed Shifted Chows (6 pts.) + No Honors (1 pt.) + Terminal Pung (1 pt.). Such hands, which allow you to build simultaneously toward Upper Four and Mixed Shifted Chows (or Lower Four and Mixed Shifted Chows), do come up occasionally, but normally you should concentrate on Upper or Lower Four. These hands are worth more points, but perhaps more importantly, they are quite flexible. For example, meld a pung of in Figure 2. This results in Figure 3, a two-chance hand with a guaranteed Upper Four.
If you see the makings of Upper Four or Lower Four, are three tiles away from making ready, and have at least two pairs, then it's a good time to consider taking action on an Upper/Lower Four combination.
In Figure 4, you would rather take advantage of your pairs and meld pungs to make Upper Four rather than go for Mixed Straight or Mixed Shifted Chows.