Rolling up to 17 dice, including 13 six-sided dice (d6), one eight-sided die (d8), one ten-sided die (d10), one twelve-sided die (d12), and one twenty-sided die (d20), the strategy of removing dice becomes nuanced due to the sheer number of dice and the varying ranges of their possible rolls. A rule of thumb—removing a die that rolls one less than its highest possible roll—can be a good starting point but might not always be the optimal choice in every situation. Here are some factors to consider:

1. High-Value Rolls: Removing a die that rolls one less than its maximum value (like a 5 on a d6, 7 on a d8, 9 on a d10, 11 on a d12, or 19 on a d20) is generally a good idea because these are high-value rolls, contributing significantly to your total score. Such rolls are close to the best possible outcome for that die, making them strong candidates for keeping, especially since you’re required to remove at least one die per roll.
2. Expected Values and Variance: Each type of die has its own expected value (EV) and variance. The larger the die (in terms of the number of sides), the higher the EV but also the larger the variance, meaning there’s a wider range of possible outcomes. When deciding which dice to remove, consider both the roll in relation to the die’s maximum value and how the roll compares to the die’s EV. For example, a roll of 4 on a d6 (EV = 3.5) is above average and might be worth keeping, especially if other dice have rolled significantly below their respective EVs. Often, you will not be left with any choice!
3. Strategic Removals: In some cases, it might make sense to remove dice that have not necessarily rolled just one less than their maximum but have still achieved a high roll, particularly if this allows you to reroll dice with lower outcomes and a higher potential for improvement. For example, if you roll a 10 on the d12 and 18 on the d20, you may choose to remove the d12, and the d20 especially when opponents are trying to stick you with taking an additional d20 on a match! 
4. Risk vs. Reward: The decision to remove a high-rolling die should also consider the balance between risk and reward. Removing a die that has rolled near its maximum value secures a high score from that die, reducing variance and risk. However, if the situation calls for a higher total score to win or achieve a certain goal, you might need to take on more risk by rerolling dice with high but not maximum rolls in hopes of achieving even better scores.
5. Opponents trying to match you: When opponents are rolling to try to match your dice, it can change your strategy. Pride and Gluttony force you to roll 3 dice once for a score, and any other sin matches force you to roll 2 dice. For penalty rolls of 2 dice, you will score a little more than 4 on average, when it’s a 3 dice penalty, it’s a whopping 7.29 points! This can affect your decision based on the risk you’re willing to take at a specific point in a roll!

In summary, while removing a die that has rolled just one less than its maximum value is often a good strategy, it’s important to consider the broader context, including the performance of all dice, the specific game rules, and the balance between risk and reward. Each roll presents a unique scenario that may warrant a different approach based on these factors.