What Are Some Advantages of Different Usages of Jokers?

The thing to remember about Lock-n-Roll is that your ability to get a high score depends largely on being able to clear the board: in the web version, you get the freedom of placing dice wherever you like (usually setting up more combos, especially if you have Jokers available), and in the mobile version, the bonuses you get for clearing a board and the ability to place all 20 dice wherever you like mean that you can repeat the process almost indefinitely, so this should be your goal at all times.

As you have no doubt discovered, it doesn't take more than a few locked dice to find yourself in an unwinnable position, especially if you have reached the point where Jokers are most expensive.

For web players

Clearing the board means that you can set up new dice however you like: your first four dice should all contribute to combos. With locked dice in place, it's much harder to place dice so that they always contribute to combos. However, without the 20-dice magic of the mobile version, there's much less of a bonus for actually clearing the board, so you have to be a bit more careful using your Jokers.

With two Jokers

As in the mobile version, you don't want to reach a point where you would earn another Joker but already have two, so you definitely want to use at least one. Your priority should be creating as many combos as possible to clear space for new dice, particularly if you can set up a Same Color Same Number combo with remaining dice. (Because you don't have to play all your dice at once, you can place a Joker in one spot to remove surrounding dice, then drop another die into that spot for your next roll.)

Using two Jokers at once isn't necessarily a good idea; a combo using both Jokers will be worth 50% less than a natural combo, and placing the Jokers so that they don't overlap usually means each of them doesn't have as much of an impact. It is generally better to use just one to knock out a reasonable number of dice and then evaluate the remaining dice based on the one-Joker logic.

With one Joker

Unlike the mobile version, you don't want to burn the Joker on a set of four locked dice, even if it would clear the board, because you don't get much of a bonus for it. Instead, you should save the Joker for at least one more roll: ideally you should be able to create a second combo with a single Joker, or possibly even three combos (which would probably require you to wait two full rolls to use it.) Your priority should be on creating Same Color Same Number combos for points (300 with a Joker), and Same Color Each Number or Each Color Same Number, again for points.

For mobile players

Clearing the board means that you get a full board of unlocked dice as well as a full sideboard, which means 20 dice to lay out as you please. That plus two Jokers means you're almost certain to clear the board again and repeat the process; even a single Joker is often enough to do the job. (Note that in a somewhat-recent update for Android and perhaps iOS as well, you accumulate Joker Coins that can be used at the start of subsequent games, either to purchase a Joker to use at the start or to decrease the cost of Jokers. The latter use can have a significant impact.)

With that in mind, there are two different strategies for using Jokers: with less than a full board (four or fewer dice to play) and with a full board (20 dice to arrange).

With less than a full board (starting position until the board is cleared)

Your primary focus should be on clearing the board; doing so will set you up to get more points than you can possibly get from a partial board. If there is any way to use your current Jokers to clear the board, do so.

Failing that, your goal should be to get four new dice so that your chances of clearing remaining dice are greater. (Remember that you do not need to place all four dice at once. This may come in handy when you can't clear everything, but want to set up the board for a possible clear on the next roll.)

• With two Jokers, as TheQ points out, the biggest risk is that you will get enough points to earn another Joker and miss out on earning it. (You do get Joker Coins, I believe, but those do not help your current game.) The best play here is to use a Joker to match dice that would otherwise not match anything else: you want those "mismatched" dice off the board so that you can attempt to match remaining dice with newly-rolled dice.
• With one Joker, while clearing dice is important, scoring points is important as well. I would refrain from using the Joker unless you will get enough points from placing it to earn another Joker ... this is more likely if you use 2 or more rolled dice in a combo. (Using 2 dice doubles your score, 3 dice triples it, and all 4 quadruples it, but your dice have to be part of the clearing combos. Placing them alone won't do it.) Ideally, you would use the Joker while also using the last of your rolled dice (even if you stick one under the Joker; remember that you can play Jokers on empty spaces, on locked dice, or on just-placed dice), so that you would get both more space on the board and four new dice to use to match the remaining locked dice. Of course, if you have no other moves, you'll have to use the Joker.

With a full board

Again, your focus is to clear the board, but it should be considerably easier, given that you can place any die anywhere.

• With two Jokers, you should always use at least one. It's neat to clear the entire board without using a Joker, and you do get points in lieu of a Joker, I believe, if you have two and earn another, but you'll generally get more points by using a Joker because you'll create more combos. Thus, you should place a Joker where it will do the most good, which is in one of the four inner squares. (These can be part of up to 7 combos.) Make sure to arrange the dice as best you can to create clearing combos based off this Joker: for example, if you have Same Color Each Number in the left column, you might switch the 2 and 3 so that the 3 is part of a Same Color Each Number row including the Joker you just placed. It's more important to clear the board than to get points, so if you have to break up a natural Same Color Same Number, do so.
• With two Jokers, it may occasionally be necessary to use both of them: this normally happens when you don't have Same Color Same Number combos to play and there is an absence of a particular color or number. Keep in mind that you may only get one Joker as a reward for clearing the board, and that you score 25% fewer points for a combo that includes a Joker, so do this only when it is necessary to clear the board: a worst-case scenario is where you use your remaining Jokers and do not clear the board; this can rapidly degenerate into the end of your game, so it's best to keep a Joker if possible.
• With only one Joker, it's imperative that you clear the entire board: a misplay could leave you with a bunch of locked dice and no Jokers to clear them. If you can't clear the board, then place the Joker in a spot that gives you as many combos as possible (again, typically in an inner square), so that you're more likely to earn another Joker to use to clear the remaining dice.

In practice, I've found that using only one joker when the playing field is stacked is actually much more beneficial.

Since you get jokers slower as time goes on, the likelihood of getting another right when you need it diminishes as the game goes on, while the luck factor of the die rolls does not change.

Otherwise, I think you're correct in "waiting for the board to fill" and then using a joker. You maximize your output for the board when you drop a joker on a space where all of the combinations can benefit from it (line, square, corners, etc).