What percentage of Call of Cthulhu characters start drowning on average?

Question

In Call of Cthulhu 7e, it is possible to call for a swimming check that can result in drowning. Assume that 80% of characters have a 20 in swim, and 20% of characters have a 60 in swim. Assume that constitution and all other ability scores are random (3d6 × 5).

What is the total chance that a single character who is called to do a swimming check will enter the drowning state assuming no outside factors help?

I am not looking for an explanation of how to run the game to avoid the swim check or how to handle swim check failures. I am just looking for the pure number and the math behind that number.

Answer 1

63% start drowning, 54% drown

For this answer I am assuming the investigator is not insane, is in his 20s or 30s (no changes to rolled CON) and the swimming is of regular difficulty. Interestingly, the rules make no notice of clothing affecting the difficulty level of swimming. We assume that an investigator who "has fallen into turbulent water" had no time to undress, and regular difficulty applies to swimming in clothes. We also assume that no help is forthcoming, as per your conditions.

For the record, I feel that your concern about the probabilities is misplaced, as the game's intent clearly and strongly is that the keeper can and should keep the character alive even if they can let them drown according to the dice rolls, so the probabilities do not really matter. But you are asking explictly about the mathematical probabilities, so this is what I'll give.

The investigator

Assume that constitution and all other ability scores are random (3d6 × 5).

• CON: 3 * 3.5 * 5 = 52.5

Probabilty to make CON roll: 52.5%
Probablity to fail CON roll: 47.5%

Event chain probabilities with outcome

All swimmers that failed their CON or pushed roll started drowning, which is not the same as drowned, in case safety can be found by successfuly pushing after a failed CON roll.

Bad Swimmers

Assume that 80% of characters have a 20 in swim

• Swim success: 20% survive
• Swim fail, CON success, pushed success: 80% * 52.5% * 20% = 8.4% survive
• Swim fail, CON fail, pushed success 80% * 47.5% * 20% = 7.6% survive
• Swim fail, CON success, pushed fail 80% * 52.5% * 80% = 33.6% drown
• Swim fail, CON fail, pushed fail 80% * 47.5% * 80% = 30.4% drown

Total sum of survive: 36%
Total sum of drown: 64%
Total sum of started drowning: 71.6%

Good Swimmers

Assume that 20% of characters have a 60 in swim.

• Swim success: 60% survive
• Swim fail, CON success, pushed success: 40% * 52.5% * 60% = 12.6% survive
• Swim fail, CON fail, pushed success 40% * 47.5% * 60% = 11.4% survive
• Swim fail, CON success, pushed fail 40% * 52.5% * 40% = 8.4% drown
• Swim fail, CON fail, pushed fail 40% * 47.5% * 40% = 7.6% drown

Total sum of survive: 84%
Total sum of drown: 16%
Total sum of started drowning: 27.4%

Combined swimmers

Assume that 80% of characters have a 20 in swim, and 20% of characters have a 60 in swim.

Results weighted by 80% for bad swimmers, 20% for good swimmers.

Total sum of survive: 80% * 36% + 20% * 84% = 45.6%
Total sum of drown: 80% * 64% + 20% * 16% = 54.4%
Total sum of started drowning: 80% * 71.6% + 20% * 27.4% = 62.76%

The procedure

Swimming to safety (drowning):

An investigator has fallen into turbulent water and must swim to safety or drown. The Keeper calls for a swim roll with the goal “swim to safety.”

Making the roll means the investigator swims to safety and lives.

If the player loses, then no progress is made and water may be inhaled; the player must make a CON roll or his or her investigator will suffer 1D6 damage per round

This situation is already drowning: the character has swallowed water and will take 1D6 damage¹ per round. You always roll CON if you fail the initial swim roll. The procedure continues:

The situation demands a pushed roll—the only alternative is that the investigator gives up and drowns. If the player misses the pushed swim roll, the investigator is battered and half-drowned, taking 1D6 damage per round.

You always roll the pushed roll, wether you succeeded on the CON roll or not. Succeeding on the pushed roll means the investigator swims to safety and lives, because as per the rules they achieve their goal as if it would have been for the original roll. This is a bit weird as it does not matter if they already had started drowning, so it does not matter that they take 1D6 per round².

The Keeper must then make an important decision: either the investigator’s life is put on the line or the investigator is washed up later elsewhere. If the Keeper chooses the former, then the investigator will continue to lose hit points each round until saved by another investigator or non-player character. Alternatively, if no one else is around, the Keeper could waive the drowning damage and instead have the unsuccessful pushed roll mean that the investigator has washed up on some foreign shore, bereft of all possessions and in a bad way.

If the investigator fails their pushed swim roll, they will be drowning no matter what, whether or not they made their CON roll, as they now take damage as per the drowning rules. (We assume this is your choice as keeper, otherwise the whole exercise here has no point), and no further progress is to be made. No option of continuing swimming to safety is given, only the option of being saved by others. Either the character is saved by someone else, or he will die in the third round if they failed their CON roll, or two rounds later, if they made it. As we assume nobody is saving them, they drown either way.

Relevant Rules

Opposing Skill/Difficulty Level

The Regular difficulty level (requiring a roll of equal to or below the skill value) is the default roll.

Pushing the Roll

Pushing a skill roll provides the player with a second and final attempt to achieve a goal. A pushed roll is only allowed if it can be justified, and it is up to the player to do this.
Pushed Roll: Success The player’s goal is achieved as it would have been for the original roll. None of the consequences of failure happen.

Other forms of Damage

Asphyxiation and Drowning: a CON roll should be made each round; once a CON roll is failed, damage is sustained each round thereafter until death or until the victim is able to breathe. If the character is in a state of physical exertion, a Hard success is required on the CON roll.

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¹ One question is if drowning damage follows the rules for Combat Damage. If yes, on a roll of 5 to 6 (damage equal to more than half maximum hit points) then a separate CON roll would be called for; if failed the character would fall unconscious, could not swim and would drown outright. However, the rules text for Major Wound: Effects is this: A Major Wound results when an attack delivers an amount of damage equal to or greater than half of the character’s maximum hit points in a single attack , and as drowning is not an attack, I think this rule can be ignored here.

² If you instead assume they take damage every round while swimming to safety, then it will matter if they made their CON roll. If they did not, hit points influcence how long they survive swimming and drowning. According to the combat rules, taking an action that requires a roll takes up a round, so the pushed swim roll takes up the second round. With average stats also for size, an ivestigator would have 8 hit points, and on average will die in the third round, unless someone intervenes or they reach saftey before then. Without a probability of that being the case, we cannot asses the overall probablity. But it would at best be as good as the numbers above.

Answer 2

As many as are needed to advance the plot.

Drowning, as you illustrate with the fact that you asked this question, is mostly a game of dice (my group refers to this as "rollies"). You make the player roll a few times, and their investigator possibly dies. This is immensely uninteresting if used too often, and harms rather than helps the story that CoC is trying to tell. Thus, I challenge the frame of your question:

Not everyone who goes into water makes a roll.

Call of Cthulhu more than most games requires the Keeper/GM to make judgement calls for the sake of dramatic tension. In some - I dare say most - cases, drowning an investigator is far less interesting than causing them to lose a valuable item, or get attacked by a Deep One, or get arrested for disturbing the peace, or - you get the idea. Death may be cheap in Call of Cthulhu, but the Keeper should still spend his allotment of player deaths wisely - on monster encounters, not big puddles.

That's not to say that actions don't have consequences.

If the cultists are hiding in an underwater base, then sure, a high-stakes underwater swimming maneuver calls for some tension in a couple of rolls. If your players start stretching credibility with how often they gallivant in the deeps, then sure, you can begin introducing difficulties to slow them down - inquisitive policemen, monsters, passers-by, crocodiles, et cetera. But rolls exist to serve story, not the other way around.

Answer 3

Not a Number %

The answer is undefined. The answer is InvalidOperationException.

"When I play Call of Cthulhu 7th edition and pre-decide the consequences of a failed pushed roll, what are the odds the pushed roll fails and the consequences come to pass?" seems to you like a very sound and reasonable question, I'm sure, but it's not.

You cannot, simultaneously, play Call of Cthulhu 7th edition and pre-decide the consequences of a failed pushed roll, any more than you can divide by zero. It isn't possible. You're breaking the rules.

Specifically, you're breaking these rules:

Dice Rule 2: Dice don't tell stories; people do.

The dice do not decide what winning or losing means in your story; that's the Keeper's job. When a player wins a skill roll, his or her goal is achieved (as agreed before the roll), but when they lose, the Keeper decides what happens.

Dice Rule 3: Losing a roll doesn’t necessarily mean failing the goal.

There are two possible outcomes of a skill roll: win or lose. It is important to realize that losing a dice roll does not automatically lead to failing the task.

Things go the way the player wants when a Pushed skill roll is won (the player's goal is achieved). When a player loses in a Pushed skill roll things go the way the Keeper wants (the goal may or may not be achieved and additional negative consequences occur).

One of the keys to running a good game is learning to define how winning or losing a dice roll translates into events in your story. Describe the outcome, not the dice roll.

If the player loses the roll then you get to decide what happens. Problems can arise if you declare an outcome that blocks play.

Dice Rule 4: Dice are used to determine who tells the story.

On winning a skill roll, the player gets to say what happens next. What the player can say has already been agreed with the Keeper when the goal was set. If you feel that the player is overstepping the mark (going far beyond the stated goal) you may veto the player’s comments, perhaps calling for a subsequent dice roll.

If the player loses a dice roll, you have free rein to describe any outcome you wish. Usually this will mean that the player's goal is not realized; however, you are not constrained to presenting the opposite of the player's goal -- the player's goal could be fully or partially achieved along with a consequence. The Keeper's job is to create an interesting outcome, preferably one that develops the theme of horror in the story.

-- "Playing the Game: Rolling Dice", CoC7E Keeper's Rulebook, pp.194-195. The emphasis on the entire final paragraph is mine.

p. 195 also includes an interesting sidebar, too long to reproduce in full, where an investigator fails a pushed Locksmith roll to pick open the only exit to a sealed room rapidly filling with water. The Keeper goes on to create an interesting outcome, which is not the investigators' collective death by drowning.

A question to consider, though its answer is just as undefined, is "in what percentage of situations where the investigators' collective death by drowning is a possible outcome is it an interesting outcome?" Its answer is undefined because the denominator can't be accurately measured. But I can't imagine that the numerator is anywhere near as large.

Answer 4

I don't have Call of Cthulu, so I'm making a few assumptions from this and its related question. Specifically, I'm assuming that having a skill/stat of "x" means you have an x% chance of succeeding (eg., having a swim of 20 means there's a 20% chance of success; having a CON of 50 means having a 50% chance of succeeding on a CON roll).

Further, I'm assuming that the order of operations is:

1. roll swim; on success, we're done: the Investigator gets away
2. roll CON; on success, we're done for the round: the Investigator lives for another round
3. roll swim; we're done: on success, the Investigator lives for another round; on failure, the Investigator either dies or finds themselves washed up on a shore somewhere

80% of characters have a 20 in swim; 20% have 60. The "average" character will have the weighted average of the two values.

20*0.8 + 60*0.2 = 16 + 12 = 28

So, the average Investigator will succeed at a swim check 28% of the time.

Finding the average CON is a bit harder, but this AnyDice program (output 3d6 * 5) can help with the odds. There's a 0.46% chance of rolling a 15 or a 90 (each), 1.39% for a 20 or 85 (each), etc..

"output 1",52.500000000024144,14.790199457750962,15,90
#,%
15,0.462962962963
20,1.38888888889
25,2.77777777778
30,4.62962962963
35,6.94444444444
40,9.72222222222
45,11.5740740741
50,12.5
55,12.5
60,11.5740740741
65,9.72222222222
70,6.94444444444
75,4.62962962963
80,2.77777777778
85,1.38888888889
90,0.462962962963

Throwing that into Excel and calculating =A18*(B18/100) for each row gives a weighted average CON of 52.5. So, Investigators will succeed at their CON roll 52.5% of the time.

Then, they have their second swim roll, which is the same 28%. Note: this is the part that I'm the least sure about; I couldn't find anything that suggests the odds are different for a pushed roll, but I didn't find anything stating that they were the same. I'm assuming they're the same, but it'll be easy enough to slot in a different number if need be.

I found a probability calculator that easily calculates conditional probabilities. The probability of failing the swimming roll then passing the CON roll ("B occurring but NOT A") is 37.8%; the probability of failing both ("neither A nor B") is 34.2%. Taking that "neither A nor B" for the new "A" here, we get the odds of failing the initial swim roll, the CON roll, and passing the second swim roll ("B occurring but NOT A") at 18.4%; the odds of failing all three rolls ("neither A nor B") is 47.4%.

All together, that puts the odds of succeeding at at least one of the rolls at (100 - 47.4) 52.6%.

I don't know what tools the players have to change those odds (the other question mentions spending luck). However, plugging in new numbers should be relatively straightforward. But, if my understanding of the basic rules is correct, an Investigator will, on average, "die" 47.4% of the time they find themselves in a situation that requires swimming to safety; they'll make it through to the next round 52.6% of the time.

The major, unanswered question is how many rounds they'll need to make the checks. This tells us the odds of succeeding on two consecutive rounds ("A and B both occurring") is 27.7%. Going to round 3, the probability of success ("A and B") is down to 14.6%; round 4 is down to 4% chance of survival.

So, what percentage of Call of Cthulu 7e characters start drowning on average? In the first round, 47.4%; in the 4th round, 96%.

Stay out of the water.

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How do I make water less lethal? The best advice I can give here is to tell the players right from the start that water is lethal and that it will feature prominently in the campaign. Let them decide that maybe their bookworm of a professor swims laps every day, that their "dumb jock" character is captain of the swim team instead of the football team, or that their character is just particularly hale (and, thus, has a higher CON than one might expect from their background).

Without doing a full re-analysis, bumping the swimming skill up to 40 means Investigators will succeed at one of the two initial checks ("A or B") 71.5% of the time.

This Google Docs spreadsheet should calculate the odds of an Investigator surviving for 5 rounds. You'll need to make a copy, but you can then edit the Swim and CON scores to play around with percentages.