Initiative and Bonuses, an important aspect of combat

Original Version (1974)

In the very version of Dungeons & Dragons (1974), initiative would be rolled with 1d6 and you would add your Dexterity bonus which was limited to +1 when you had an ability score of 13 or more. There is the Dexterity bonus table:

to Hit
3-8 -1
9-12 0
13-18 +1

Such a small bonus would not affect the roll very much, although with a 1d6 it had a larger effect than in newer versions of D&D that use a 1d20 to roll initiative.

Also one party would be allowed to add the bonus only if all the foes on one side had the same bonus. In other words, if your thief had 18 in Dexterity but your Magic-User had 10, you could not add the +1 to the initiative roll.

So you would think that in most cases the bonus would benefit monsters... only in that very first version monsters were not given scores for each one of their skills. So we did not have that information. In other words, we would always use 0 for the monsters.

However, as a result, the authors of the very first version decided that the -1 did not have to be applied either. So the party of characters would either have a +0 or a +1.

As a result, the difference was quite minimal. When a party had the +1 bonus, they would be ahead of the monsters by 1/6th or an increase chance of winning initiative of 16.67%. Remember that in this version the players were probably expected to play simultaneously when they both rolled the same number (it was not clearly defined, but was described as such in a Dragon magazin) which is why the odds change exactly by 1/6th for the +1 bonus.

Note that there would be one case where the monsters would eventually have a bonus: in the event the characters where attacked by an evil party of Fighting-Men, Magic-Users, etc. since those would have scores and we could determine whether they all had a high enough dexterity to gain the +1 bonus.

The documentation had an example about initiative with Orcs and they say that they would have a -1 on initiative. Unfortunately the monster descriptions did not include that information.

Advanced Dungeons & Dragons 1e

The Dexterity bonus was dropped and no other bonuses applied. In this version we would just roll 1d6 and hope to roll a higher number to have initiative.

In other words, this was using what we call pure luck.

Advanced Dungeons & Dragons 2e

This version introduced many different types of bonuses that could be applied to your die, but not your Dexterity Score bonuses.

It also changed the die to roll: 1d10.

Contrary to the previous versions, Hasted and Slowed did not automatically make you win or lose initiative. Instead it was converted to a +2 or -2 bonus on your 1d10 roll.

The other modifiers were in link with position (higher/lower), footing stability (solid rock/muddy), hindered (blocked in some way, i.e. tied up or doing something that prevented you from using your full ability like climbing rocks). Optionally, you could use the weapon modifier, the spell casting time, and the size of a creature to also affect the roll.

The bonuses could go from about -7 to +18, which was a very large amount on a 1d10. So you could roll a number from 1 to 10 and add your bonuses resulting in a number between about -6 to +28. In other words, 35 possibilities.

The results were difficult to predict. For sure, if you had a slow weapon or spell, you were likely to strike later in the round. Although at this time you would still re-roll initiative on each round. That would give you that small extra chance of winning initiative once in a while.

Side Note: Initiative in this version was reversed. The ones with the smallest roll + bonuses would go first.

Large monsters, such as Giants and the Tarrasque, were very likely to end up hitting last because the size bonuses were quite negative for them, with the gargantuan receiving a +12. You could actually end up striking first even when you rolled a 10 and they rolled a 1! The most powerful foes, though were not automatically very large...

Dungeons & Dragons 3e and up

Since the Third Edition of Dungeons & Dragons, initiative is rolled using 1d20 and adding your Dexterity Score bonus to the die roll.

It is at times called a Dexterity Check since it is similar to rolling such a check. However, specific bonuses get added to the Initiative Roll, which would not apply to a Dexterity Check, so it is not 1 to 1 equivalent.

On top of your Dexterity and depending on the version some other bonuses apply. For example, a feat may give you a +10 bonus, a percent of your level may be added to the roll, etc. So in terms of bonuses we may get something somewhat similar to what we had in Second Edition of Dungeons & Dragons. However, most of the bonuses that could be applied to Initiative were not as high at lower levels, except for the Dexterity Score bonus which could be as high as +5 (and as low as -5, but who put 3 in their Dexterity Score now?) Bonuses you could get right from level 1.

Adding a bonus depending on the character level makes a lot of sense since as you grow in experience you also learn to fight better and thus can gain various advantages over your attackers. You will know of more and more tricks to get your sword out quickly, get in the right position, and strike as soon as possible.

A 1d20 roll gives you a linear chance of 5% per number on the die. The bonuses translate those chances down (negative bonus, you get a worst result) or up (positive bonus, you get a better result.)

A high Dexterity Score gives you a positive bonus right off the bat. This can increases your changes between 20.24% (+1 bonus) and 45.46% (+5 bonus) depending on the version of D&D you are playing. It will matter less and less as you grow in levels because many other parameters enter in account and monsters become stronger and also have quite nice initiative bonuses. However, for low level characters, having a really high Dexterity is a quite nice feature since it gives you a much greater chance to start early in each combat round.

However, all of those versions require initiative to be rolled only once at the beginning of combat then everyone plays one after another in the same order, round after round, for that entire combat. Although the order can change over time, whenever someone uses an action that allows them to switch to a different spot in initiative order, the initiative roll has no real effect once you are on futher combat rounds.

So the bonuses are great to get the very first hit in combat and that can be really useful on the very first round for low level characters (level 1 to 3 or so) since a hit on the very first round on a an enemy such as a Kobold or a Giant Rat can kill the enemy at once. Not only that, if you kill a couple before the enemy can fight back, they may end up running away so you do not risk getting killed...

Calculating the Gain or Loss with +n Bonuses Over Your Adversary (3e+)

The gain or loss over your adversary is not linear even though you get what looks like a linear bonus.

When both adversary have the same bonus, they both can win 50% of the time. There are 190 cases when you can win, another 190 cases when you can lose, and 20 cases when you are expected to reroll.

For each +1 bonus of the adversary, you lose one reroll (so at +1 you have 19 rerolls.) However, the number of wins increases by +20 with +1, then +19 with +2, +18 with +3, etc. The loses decrease at a similar rate, at +1 you decrease by 20, at +2 you decrease by 19, etc.

So the resulting curve is not linear and also your chances continue to grow, they grow slower and slower. That being said, at some point (i.e. +19) you always win Initiative. Note that at +19, no roll is necessary since the person with +0 could roll a 20 and the person with +19 could roll a 1 so both would get a 20 initiative. You'd have to reroll any number of times to break the tie and the only possible result in that case is that the person with +19 is always going to win Initiative.

The following graph shows that the increase of your chances to win initiative grow drastically with a +1 and +2, but not as much with you have +10 or +15. Of course, it is still a great advantage to have such numbers! It still makes you much more than likely to win initiative. It's just doesn't make a huge difference to have +14 or +15 than it does to have a +0 or +1.

Graph showing how initiative is affected by bonuses from +0 to +20.

Note: applies to Thrid Edition and newer since the calculations were made using the 1d20 rules.

The graph has a red line showing how the curve would look like if it were linear and each +1 was increasing the chances by exactly 5%. At +10 you would always win if it were, which is obviously wrong (although with 88.46% against 11.54% you're already likely to win Initiative pretty much all the time; you actualy have 76.92% more chances to win.)

With a bonus of +0, chances are 50% on both sides. Sorry... The graph does not show those numbers. The "5" in the graph vertical axis represents 100% chances which means the last two columns: 19 and 20.

The following table shows you the percentages to win or loss initiative with a corresponding bonus. Note that the bonus shown here is the difference between the largest and smallest bonuses of two opponents. So if a dragon attacks and has +20 and your character has +7, the davantage is to the dragon with +13.

Bonus Winner Loser Winner
Extra %
+0 50% 50% +0%
+1 55.12% 44.88% +10.24%
+2 59.95% 40.05% +19.90%
+3 64.49% 35.51% +28.98%
+4 68.75% 31.25% +37.50%
+5 72.73% 27.27% +45.46%
+6 76.42% 23.58% +52.84%
+7 79.84% 20.16% +59.68%
+8 82.99% 17.01% +65.98%
+9 85.86% 14.14% +71.72%
+10 88.46% 11.54% +76.92%
+11 90.79% 9.21% +81.58%
+12 92.86% 7.14% +85.72%
+13 94.66% 5.34% +89.32%
+14 96.19% 3.81% +92.38%
+15 97.47% 2.53% +94.94%
+16 98.48% 1.52% +96.96%
+17 99.24% 0.76% +98.48%
+18 99.75% 0.25% +99.50%
+19 100% 0% +100%
+20 100% 0% +100%

As we can see, with +19 over an adversary, you always win initiative. This is why really high level foes generally wins over 1st level. They have one blow and it's going to be a deadly blow! (i.e. you don't even go in a coma, you just die right there.)

What About Ultra Initiative?

Using Ultra Initiative in 3e, 4e, or 5e means re-rolling initiative on each round. If you do not have too many players or your players are well versed in the game, it should be really fast to do it this way.

In the original version and the Advanced Dungeons & Dragons 1e and 2e, we were rolling the initiative dice on each round. This is where this method comes from.

What does that change in your combat?

If both parties have about the same modifiers, then it is likely that people who go first will ping-pong between each round.

When one party has a much greater modifier, then it gives a chance to the other to run first once in a while.

So say you have +7 over your adversary. You have 59.68% more chances to win initiative. That means your adversary may go before you once every 3 or 4 rounds. Well... if the roles are reversed and that's your adversary, it gives you a chance to go first once in a while.

Having played Advanced Dungeons & Dragons, I prefer this method. I think it adds excitment to the game. Only you need to train your players to roll their die quickly at the end of each round so we can quikcly start the next round.

Last Words to the Dungeon Master

Note that your games are just expected to be fun! Whatever the odds your dice give you.

As the Dungeons Master, if you think that your players are going to lose a combat, changing the odds in their favor in some other way is probably a good idea. Maybe they get teleported against their will or maybe you wanted them to die so they can get resurrected by that evil cleric... as zombies!

Just remember that if you are not using Ultra Initiative, in the newest versions of D&D (3e+), the order is fixed so you can't really change the odds that monsters will continue attack on their turn. That being said, maybe one could start eating a character instead of attacking another character. Especially if all the characters are currently busy with another foe anyway.

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