Can You Roll a D20 Instead of 5d4

In 5th Edition D&D, a character's starting equipment is primarily determined by their class. Players can choose from a list of equipment or roll starting gold to purchase their equipment.

This sort of exchange seems normal. Except, the gold value doesn't really match the value of the starting equipment.

Variance

We're not going to have an exact fit, since there is variance for both chosen equipment and rolled gold.

Variance in Chosen Equipment

If you choose to take the equipment, you may be offered a selection of different equipment. This isn't always an equal trade in terms of value.

For example, a Fighter is offered the choice between light crossbow and two handaxes. Even before factoring in the free ammunition that comes with the crossbow, its value (25 gp) is significantly higher than the handaxes (5 gp each).

Oftentimes you'll be offered a choice of a class of weapons, such as any martial melee weapon. In this case, you can maximize your value by taking the most expensive option in the class, although it might not be the best option for your character.

Variance in Rolled Gold

As expected, there's variance in rolling your gold. If you choose you roll, you will roll a certain number of d4s. Then, you multiply the result by 10 (except in the case of the austere Monk). Rolling more dice makes rolling average more likely.

Odds of rolling at least a certain amount of gold with 2/3/4/5d4 x 10:

Choice

If you choose equipment, you can select for the maximum equipment value. You may not because you like cheaper equipment to fit your character concept, but you have access to the maximum gold value if you want it.

If you choose to roll gold, you will likely get the average amount. That's because the results of multiple dice will trend towards the middle. You can see this in the charts above, where you have a very high chance of rolling up to the average, then a very small chance of rolling the highest result.

Comparison

In order to form a basis for comparison, I tallied up the maximum, average, and minimum values for chosen equipment and rolled gold.

Because choice is in our hands with chosen equipment, we take the maximum value for comparison. For example, if a barbarian gets a choice between a greataxe (30 gp) and any martial weapon, they will take a greatsword (50 gp). If you're curious, greatsword was a better choice anyhow.

Because we don't have the choice of value when rolling gold, we take the average value for comparison. We do this by taking the midpoint of the lowest and highest die roll.

Here's how the maximum chosen equipment value stacks up against the average die roll:

The two columns at the end show you how rolled gold stacks up vs. chosen equipment. The first column shows average rolled gold as a percentage of maximum equipment value. The second column shows the raw difference between maximum equipment value and average rolled gold.

Expectations

Before we jump into the analysis, let's set our expectations.

We shouldn't expect the value of equipment and rolled gold to be equal.

There's value in variance. Cash is king. You can use it to buy anything. You aren't locked into the limited choices provided in the starting equipment list. So there should be a premium on rolled gold.

At the same time, the gambler should get an outside shot at rolling higher value than the equipment choices. After all, they are risking rolling a lower equipment value.

Let's follow these guidelines:

1. The average rolled gold should be less than the maximum equipment value.
2. The maximum rolled gold should be more than the maximum equipment value.
3. Neither of these differences should be significant.

Analysis

Martial classes do very poorly! Fighters (48%/-138 gold) get the biggest pay cut, followed by paladins (49%/-129 gold). You'd think this might be a result of armor, but look at monks (33%/-25 gold) and barbarians (57%/-37 gold).

Bards (112%/+13 gold) and sorcerers (114%/+9 gold) are the only classes whose average gold rolls outperform the max chosen equipment. If you're playing either, you should roll your gold and buy your equipment.

The closest match are rangers (94%/-8 gold) and rogues (95%/-5 gold).

Other close matches are the artificer (77%/-38 gold), cleric (83%/-25 gold), warlock (78%/-29 gold), and wizard (85%/-17 gold), who all range between 75% and 86%. While not very close to the maximum equipment value these are all in fair range. If you place a higher value on flexibility, you might think that this range is more fair than a closer match.

Finally, the druid (63%/-30 gold) sits in an odd spot. The actual amount of the gold difference is close to the warlock. While not an equipment-dependent class due to Wild Shape, it could probably stand to use a boost from 63%.

Tweaking Gold Dice

In order to fix these disparities, we can adjust the number of d4s each class rolls for their starting gold. Here's a handy chart:

Using 80% of the max chosen equipment value, here's the adjustments:

• +3 Gold Dice: fighter and paladin.
• +1 Gold Die: barbarian and druid.
• -1 Gold Die: sorcerer, ranger, rogue, and bard.
• No Change: artificer, cleric, warlock, and wizard.
• Special: monk.

Monks

The monk is a special case. We're giving it back the "times 10" multiplier like every other class, and just limiting it to one gold die. This is a lot more swingy, but also a lot more likely to get the monk a decent set of starting equipment. They can't even buy their minimum starting equipment with a max gold roll under RAW. There's little concern for excess because even a max roll is only 2.5 gold more than the monk's maximum equipment value. Also, there's a lot to be said for the consistency of having the same mechanic for every class rolling gold (i.e. xd4 * 10).

Maximum Gold

One unintended side effect of adjusting these values is that it raises the potential cap on starting gold. With 8 gold dice, the fighter and paladin now have a gold cap of 320 (up from 200). However, it's worth noting that the odds of rolling this high are very small. The odds that the paladin rolls enough gold to buy its max equipment is only 4%; the odds the fighter rolls enough to buy its max equipment is less than 2%.

Minimum Gold

Meanwhile, we're setting a reasonable floor. The odds the paladin rolls enough to buy its minimum equipment is over 86%; the odds the fighter rolls enough to buy its minimum equipment is over 92%. There will always be some variance with rolling, but it wouldn't be fun without any risk. When we compare with the RAW method of rolling gold, the paladin and fighter have over 56% odds to roll better than the max starting gold they get by the book (200 gp).

If you want more analysis check out the ThinkDM Patreon, where you can find a full chart that lets you adjust gold based on % of max starting equipment value, configure the starting equipment for each class, and use different gold dice.

Can You Roll a D20 Instead of 5d4

Source: https://thinkdm.org/2019/12/28/starting-gold/

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