- Rule 1 - Agree ahead of time with your opponents about what situations will require rerolls.
- Use a dice tower or cups. Cups are better with up to six dice, and there's very little chance of getting a cocked die.
- I don't mind using a phone app for die rolling (especially solitaire) but I would not use one in a competitive situation, such as at a tournament unless the tournament was held online. Just a little too easy to rig them if you've got coding chops.
- Use dice from the same lot if at all possible. I got a Perudo (Liar's Dice set) years ago with five dice in each of six colors with cups that is a staple when we play. The weighting should be about the same and thus even if they aren't perfectly balanced you should get similar results for all players.
- The most balanced dice are big casino dice. Weight and size are the best way to achieve balance in a die if that's a concern.
- No matter what method you use, a determined cheater will find a way to skew the results their way. If you are fairly certain an opponent is cheating, ask them if they would mind if they used another method for rolling. I was actually accused of this once after a really good round of dice at a game at WBC ten years ago, and once people started looking at me funny I simply told them that I did not cheat under any circumstances and that I was happy to let them decide how my dice would be rolled (even by someone else) and they relaxed quite a bit after that. My dice going stone cold after that point did not hurt either.
- If you roll too many dice in any situation, the entire roll is rerolled.
- If you roll too few dice and are using a cup, set aside the rolled dice and roll the extras. If you are using a tower, toss the extra dice in and accept any resulting changes to already rolled dice that get hit by the new dice.
- If you are ever in a situation where you and your opponent disagree about what to do with a die, roll a die (or pick a hand with a counter or die in it) to determine whose interpretation is the right one. Be consistent from that point on if the situation comes up again.
- Don't lawyer situations to your advantage, but instead focus on consistency and fairness.
- Even if you are playing solitaire against a "system" (and thus can win or lose the game), have a set of rules for ambiguous dice that you use by default.
Some rules for cocked and "escaped" dice:
- Agree ahead of time what constitutes a cocked die. I prefer dice to be laying flat on a single surface (or partially on a thin sheet of paper) to be "legit" but YMMV.
- If using a tower, decide if "escaped" dice qualify for rerolling. If there are a lot of dice being rolled, I prefer to just accept the roll. If there are a small number of dice, I reroll them if they escape, keeping the existing dice in the tower as for rolling too few dice above.
- If using a tower and you get a cocked die, bump the top of the tower straight down. This will "flatten" dice that are "close" to being perfectly flat but up against a wall or another die.
- If using a tower and the die is seriously cocked (near a 45 degree angle from flat) I will pull the die and reroll it if possible as with rolling too few dice above.
- If I can't easily extract the cocked die, or if there are too many dice cocked to do this adequately, reroll the whole thing. If this happens more than once in a game, you are rolling too many dice at once and you need to consider rolling fewer at a time.
If you are playing a solitaire game, especially where you are playing two sides against each other and are playing to learn the system, feel free to "cheat" if you think it would result in a more interesting or educational situation.
In a tournament or other competitive situation, unless there are specific rules governing ambiguous dice rolls you should most definitely get in the habit of agreeing on what to do up front. If you have a problem with your opponent or you run into regular situations where you don't agree, seek the assistance of the GM or referee, that's what they are there for.
Kind of anal? Maybe. But I've found that the more transparent you are about this kind of situation up front, the more enjoyable the game is because both players know neither is going to try to turn an ambiguous situation to their advantage because you've dealt with it up front. In a friendly game with a familiar opponent, it's less important (depending upon your opponent), and almost any disagreement is easily solved with a die roll.