Leafiara (prime)/Mechanical Musings/Expected Value
Title: Expected Value
Author: Leafiara
Date Published: 2025-10-03
Updated: 2025-10-03
By Leafiara Autumnwind.
Last updated October 3, 2025.
Feel free to message me on Discord, send a thought, send player mail, or otherwise get feedback to me.
Scope and Purpose
How do we identify whether entering a raffle is a winning or losing proposition, mathematically speaking? In more layman's terms, when should we enter a raffle?
This guide seeks to provide a framework for more objectively answering these core questions that come up during numerous GemStone festivals and pay events. I've written it primarily for three demographics:
- Players with very limited amounts of silver trying to decide how to spend it
- Players who enter every raffle that exists
- Players who ignore every raffle that exists
The first group "needs" calculations the most, but we can all benefit from understanding the numbers.
The second group can sometimes just subjectively enjoy winning without stopping to consider whether their wins are even beneficial over time, which might or might not be the case.
The third group frequently assumes they'll lose every raffle without stopping to consider how many raffles they'd need to enter on average before winning. (Like with my monk guide, I actually considered dedicating this one to Saraphenia too. She became disillusioned and was in that third group, not having much of a stomach for raffles, until I talked her back into trying by explaining--in highly abbreviated fashion--everything you're about to read on this page.)
As for myself, I typically enter 20-60% of raffles at a given festival--and the rest of this guide explains my methodology for why and which ones.
An Extremely Simplified Example
Math is hard, so we'll start with barebones basics.
Imagine a GemStone raffle where you can pay silver to win silver. Its tickets cost 100,000, it draws one winner, and the prize is 100,000,000. Under what circumstances should you enter it?
The short answer is that:
- You should enter if fewer than 1000 people enter
- You shouldn't enter if more than 1000 people enter
- You neither should nor shouldn't enter if exactly 1000 people enter (the 1000 figure includes you)
This simple example might seem intuitive at first. With a straightforward payout of 1000:1, it would naturally make sense to enter if the odds are 1:999 or better and skip it if the odds are 1:1001 or worse, right? Well, yes, that's right--if we have to treat the answer as a binary yes or no.
But how clear-cut can the yes or no actually be? And what do I mean that you neither should nor shouldn't enter when the odds are exactly 1:1000?
Enter the main subject of this guide...
Expected Value
Expected value (EV) is the average profit or loss you would expect to incur from a raffle ticket based on its cost, the value of its prize, and the odds of winning.
For now, we'll stick with our pay-silver-to-win-silver raffle example. Again: 100,000 is the ticket cost, there's one winner, and the prize is 100,000,000. You calculate the expected value by subtracting all losses from all winnings, then dividing the result by the number of tickets.
Let's first deal with my point about how you neither should nor shouldn't enter if you'd be one of exactly 1000 entries. In such a case:
- One person wins 99,900,000. (The prize is nominally 100,000,000, but the winner also spent 100,000 to acquire it.)
- 999 people lose 100,000 each, which is 99,900,000 collectively.
Expected value: (99,900,000 - 99,900,000)/1000 = 0/1000 = 0.
So there's no net benefit nor loss. If this raffle repeated endlessly and the same 1000 people entered every time, they would all break even.
When the odds and the payout mirror each other exactly, there's no mathematical justification in a vacuum for or against entering. (However, there could still be other justifications from additional factors. For example, an argument in favor could be the enjoyment of having your name pulled and an argument against could be the required time spent to enter. More on this later.)
What if only 999 people entered? In such a case:
- One person wins 99,900,000.
- 998 people lose 100,000 each, which is 99,800,000 collectively.
Expected value: (99,900,000 - 99,800,000)/999 = ~100.1.
In this example, if the raffle repeated endlessly and the same 999 people entered it every time, they would make ~100.1 silver per ticket on average.
So, everything considered in isolation, EV tells us that the mathematically correct move is entering.
However, if we bring in complicating factors, the correct move might still not be entering. For example, consider opportunity cost; if a character could have made more than ~100.1 silver via other activities in the same amount of time as or less time than it would take to enter the raffle, then entering the raffle no longer makes sense! (Mathematically.)
Let's alter the numbers more drastically and say only 300 people entered. In such a case...
- One person wins 99,900,000.
- 299 people lose 100,000 each, which is 29,900,000 collectively.
Expected value: (99,900,000 - 29,900,000)/300 = 233,333.333.
This time, the expected value is very high! You would profit (not net, but profit) 233,333.333 silver per ticket on average if you could enter this raffle infinite times under the same conditions. Complicating factors would have to be extraordinary to make a case against entering the raffle! For example, maybe if you have to be online by waking up three hours earlier than usual for the raffle, that amount of silver isn't worth it.
Raffle Timing Strategy
For GemStone raffles in which you can see the number of entrants (which is most of them), EV gives us grounds to delay entering for as long as we can to make the most informed possible decisions.
Until now, we've been looking at hypotheticals where we already know the final odds. For participation in live raffles, however, only the last person who enters can calculate the precise expected value! Depending on the total number of tickets purchased, the last several dozen entrants might also subjectively be considered close enough to make informed decisions, especially if they estimate the final number to be a bit higher than it is at the time they enter the raffle.
Conversely, the earlier one enters a raffle, the less information they have. When a player's availability and time constraints require them to enter a raffle early or not at all, one thing they can do is model out scenarios like calculating the EV in increments of 25 or 50 additional entrants to determine whether it's favorable. The upper boundary on people entering can sometimes be estimated based on past raffles that happened under similar conditions. For example, the highest number of entrants seen in a raffle at a given festival could be presumed for the next time that festival is held if the location, costs, and caliber of prizes are the same or similar.
Repeated Raffles and Practical Application with Item-Based Raffles
So far we've only looked at EV in the context of paying silver to win more silver just to get a feel for the math, but, in reality, GemStone IV almost never has silver-for-silver raffles. How does analysis change when the prizes are items or services instead?
Let's start by evaluating the value of a prize as the amount that you would have been willing to pay if the prize were available for purchase. (For the sake of this hypothetical, don't consider whether you could pay that amount, but whether you would if you had the silver. I'll explain why after an example.)
Let's say that an Ebon Gate Treasure Trove raffle is being held for a custom death message and that I'd be willing to pay 15,000,000 silver for it if I could. Of course, it's not available to buy directly, so that leaves me considering whether to enter the raffle. It has a 100,000 silver ticket price, but, since it's a Treasure Trove raffle, I can't see the number of people entering and need to estimate.
Going back to basic math, since the prize is worth 14,900,000 (15,000,000 minus the ticket cost), I should enter if I estimate that fewer than 149 people will enter and shouldn't enter if I estimate that more than 149 people will enter.
An obvious objection, of course, is to ask what the harm in trying is even if more people enter.
Self-evidently, the worst outcome from entering a raffle for 100,000 silver is losing 100,000 silver. That's the harm in trying. Taken in isolation, it's not a drastic change--but we're only looking at a single raffle and this is GemStone, where many people enter many raffles and are potentially ripping themselves off because of it. Time to illustrate!
Let's say there are 100 such raffles under the previous conditions of 100,000 silver entry fees and prizes which I'd value at 15,000,000, but, this time, each would have 500 entries (counting mine) if I entered.
Probability says that if I enter all of them, there's an ~81.85668% chance that I'll lose all of them, having spent 10,000,000 silvers to get nothing. However, the EV isn't -10,000,000 * 0.815668, which would be -8,156,680 silver. The EV is...
Expected value: (1,490,000,000 - 4,990,000,000)/500 = -7,000,000.
But why the discrepancy? Follow closely now:
Expected value calculations account for the math of both winning and losing outcomes, which means they've already accounted for the reality that you would eventually win given an infinite sample size of raffle entries under the same conditions.
When expected value is negative, it means the odds are such that by the time you would be likely to have won, you'd still actually have lost--and substantially so--because, on average, the amount you would have needed to spend to get the win exceeded the amount you believed you would have been willing to pay for the prize in the first place.
Unquantifiable Subjective Value
All our examples so far have assumed you can quantify the value of a raffle prize, but if you can't, is there still a way to objectively decide whether to enter for it?
Well, not necessarily objectively, but rationally, yes.
If it's the type of raffle in which you can see the number of entrants, you could run the EV calculation in reverse to solve for the variable of an unknown prize value. In this case, you can determine how low the value would need to be before the entry price and odds of winning make it no longer worthwhile, then subjectively guess whether the prize is worth more than that minimum.
If you can't see the number of entrants, then analysis gets trickier. You could, of course, arbitrarily assign a value to the prize, but this section presumes that you can't--and what then? Even when the prize value is unknown, the subjective value of the silver to buy your raffle ticket isn't.
The previous Repeated Raffles section discussed the potential trouble with entering raffles as a pattern of behavior over time, but it's not likely that you encounter a large number of raffles with prizes of unquantifiable value, so we can consider this scenario an isolated event. Whether the ticket costs 1,000 silver or 1,000,000 silver, the worst case scenario in that you're out exactly that much silver. How much opportunity cost or hassle does regaining that amount represent? You know the answer, which is personalized to you, so you can make a rational decision.
Multi-Winner Raffles
I haven't explicitly said this yet, but the same methodology as before applies: "You calculate the expected value by subtracting all losses from all winnings, then dividing the result by the number of tickets."
[this page and/or section under construction!]