You should be trying to make a Color Run or Three-of-a-Kind for all stones. Anything else is unlikely to win. Aiming for Three-of-a-Kind for all stones is not a bad idea. Any formation below Three-of-a-Kind is for "fallback". Only use if you know that you can win the stone or your opponent will lose it.
Preparing for a Color Run (e.g., playing a 4 on a lone 5 is a good idea (as long as the location of the 3 and 6 is unknown). This means there are two cards potentially in the deck to finish the formation, and the odds of getting one of them is high, especially early in the game. This is a better play than playing a 5 on the 5. Three-of-a-Kind is good, but if you don't get that third card, you have no safety net. If you don't get the 3 or 6, you can settle for a Run formation, rather than a Sum formation.
The exception to this is when you have Color Run cards with a gap (i.e., 2, 4 in your hand, missing the 3). Then you may want to wait as long as possible before committing.
The nine may be the highest (strongest) card, but the seven is more versatile. The three best hands you can make in the game are the Color Runs 7-8-9, 6-7-8, and 5-6-7. All require a seven. There's only one way to make a Color Run with a nine. This also means 6 is a better card than an 8. Definitely better if the 9 is already out.
Wait as long as you can for your opponent to play a first card to a stone before you do. The opponent will likely play a second card to that stone before you play your second. This gives you the advantage of information. When you must place a card on an empty stone, be aware of how your opponent can make use of the information being provided. Don't let the opponent know they can delay playing to that stone until they have what they need. Keep your options open. Once you commit to a formation, your opponent has the advantage of time to win that stone.
When the opponent plays the first card to a stone, try to play a card that is one or two higher to reserve a tie-breaking advantage. If the opponent's card is 7 or 8, wait to see what is played next before choosing a counterattack. If the opponent's card is a 9, you might as well play something low like a 3 since you can't play a higher card.
When an opponent has played two cards to a stone, and you have one, there are two good strategies to use: 1. If your card is higher than his, aim for the same formation. 2. If your card is lower than his, aim for the other formation (i.e., if the opponent is attempting a Color Run, go for Three-of-a-Kind, and vice versa). The goal is increase your likelihood of winning if neither of you get the card you need or both of you get the card you need.
If you have three ones, play them on a stone where the opponent is attempting a Color Run (e.g., 6-7). If the opponent finishes the formation, the stone is lost anyway. If not, then you will surely win.
In a full game, each player will play 27 cards, or 9 stones x 3 cards. Claiming a stone before the other player has played all three cards means they will have to retain cards they don't want. The more this happens, the greater the pressure for the player. If you have a 3 that prevents your opponent from completing a 4-5, don't end up stuck with nowhere to put it. This means try to stop your opponent from completing three-card sets and avoid being stopped yourself. Claim stones as soon as they're eligible.
Claiming three adjacent stones is the most common way to win, and this is determined early in the game. Play strong cards in a spot to break your opponent from winning early with three adjacent stones.
