The Tabletop Math Worth Trusting, and the Math That Lies to You
I build calculators for tabletop games, so it would be convenient for me to claim that every number they produce is gospel. It is not. Some tabletop math is genuinely predictive and will make you a better player the day you understand it. Other tabletop math is technically correct and still misleads you, because it answers a question you were not actually asking.
This page sorts the common calculations into those two piles. It is the guide I would hand a friend who has just discovered spreadsheets and is about to spend a month optimising the wrong thing.
The verdict table
| Calculation | Verdict | Why |
|---|---|---|
| Damage per round, comparing two builds | Trust it | Averages rank options correctly over a campaign. This is what the number is for. |
| Damage per round, predicting one fight | Do not trust it | Variance dominates a short fight. An average is a poor description of four dice rolls. |
| Encounter XP budgets | Rough floor only | They price monsters, not tactics, terrain, or the party's action economy. |
| Action economy (turns per side) | Trust it more than XP | Two monsters acting twice is a different fight from one monster acting once. |
| Deck land count and curve | Trust it | Drawing cards from a shuffled deck is a solved probability problem. |
| Monopoly landing frequency | Trust it | The board is not uniform, and the rules themselves tell you why. |
| Monopoly value by purchase price | Do not trust it | Price is not return. Return is landing frequency multiplied by rent after building. |
| Army points totals | Trust for legality, not power | Points are a balancing target the designers aim at, not a measurement of how good a list is. |
| Card "investment" value | Heavy skepticism | Illiquid, spread-heavy, and one reprint announcement from a correction. |
Averages describe campaigns, not moments
Expected damage per round is the most useful number in character optimisation and the most abused. It is an average, and an average is a statement about the long run. Over thirty sessions, the build with higher expected damage will out-damage the alternative, and the calculation earns its keep.
In a single four-round boss fight, that same number tells you remarkably little. If your attack hits on a 9 or better, you miss forty percent of the time, and missing twice in a row happens roughly one fight in six. Players who have internalised their damage average often feel cheated by perfectly ordinary variance. The fix is not better math, it is remembering what the math promised: a long-run tendency, not a guarantee about tonight.
This is also why the reliable, lower-average option is frequently the better real choice. Consistency has a value that an average conceals.
Encounter budgets price the monsters, not the fight
Encounter-building guidelines assign a value to each monster and total it against the party. That is a genuinely useful starting point, and if you are new to running games you should use it. But it is a pricing model, and it is blind to the things that actually decide fights.
The largest of those is action economy. A single high-value monster against five players gets one turn while the party gets five, and it will usually die before it does much. Split the same budget across four weaker monsters and the fight becomes dramatically harder, because now the sides trade turns closer to evenly. The budget says these encounters are equivalent. They are not, and every experienced referee knows it.
Terrain, surprise, and whether the party has spent its daily resources move the difficulty at least as much. Treat the budget as a floor you build on, not an answer.
Card probability is the honest one
If one piece of tabletop math deserves your trust without caveat, it is deck probability. Drawing a fixed number of cards from a shuffled deck of known contents is a textbook problem, and the answers are exact rather than approximate. How likely you are to have a given land count by turn three is not a matter of opinion, and it does not care how you feel about it.
This is why deck-building conventions such as minimum deck sizes and familiar land ratios have survived decades of play: they are downstream of arithmetic that does not change. When your curve is wrong, you will feel it as "unlucky" games that are in fact entirely predictable. Fix the list rather than blaming the shuffle.
Monopoly rewards geography, not price
Monopoly is the clearest case of a correct number answering the wrong question. Players evaluate properties by purchase price, because the price is printed right there. But your return comes from how often opponents land on a square and what the rent is once you have built, and landing is not evenly distributed.
The rules themselves explain the distortion. There is a square that sends you directly to Jail, and there are card decks that move players around the board. Jail therefore gets far more traffic than an ordinary square, and the properties a short dice roll past Jail get a steady stream of visitors leaving it. The mid-priced oranges and reds benefit from exactly this, which is why experienced players fight over them while a beginner is saving for the expensive blues that opponents reach far less often.
Cheap sets have the opposite problem in a different direction: rent stays low even fully built, so they win slowly. The useful calculation is not the price on the deed. It is traffic multiplied by post-build rent, against the cost to get there.
Points are a target, not a measurement
Army points exist so two players can agree on a fair-sized game, and they are excellent at that. They are much weaker as a claim about strength. Points are set by designers before the meta exists, they are revised precisely because they turn out to be wrong, and two lists at identical totals can be wildly unequal. Use points to build a legal list, then judge the list on what it actually does.
What to do with all this
The pattern across every row of that table is the same. The math is almost never incorrect. It is answering a narrower question than the one in your head, and the error creeps in during translation. Expected damage answers "over many fights," not "this fight." A points total answers "is this legal," not "will this win." A purchase price answers "what does it cost," not "what will it earn."
Ask the calculation what question it actually answers, and it will serve you well. The tools on this site show their working for exactly that reason: you should be able to see which question you are getting an answer to. If you want to run the numbers yourself, the damage per round calculator, the mana curve calculator, and the Monopoly trade calculator are the three that map most directly onto the sections above.
Sources: Dungeons and Dragons Basic Rules (Wizards of the Coast, PDF); D&D Beyond: Basic Rules; Pathfinder 2e rules (Archives of Nethys); Magic: The Gathering official rules; Hasbro: Monopoly Classic official rules; Warhammer 40,000 official downloads (Games Workshop).