new death save == leave your buddy on the floor for 3 rounds?

[catsclaw]

I just ran 100 Excel simulations - it's what I have here at the office, sue me - and got 31% chance of saving (which I'll accept as just a rounding error on your 25% solution) with an average turn of 6 for the death (which is where your data peaks over 50%).

Hrm. That's an awfully high rounding error.

FWIW: I've put a simulation up at Google Spreadsheets. Should be self-explanatory. Unfortunately, Google Spreadsheets are pretty limited so there's only 230 runs. And there's no easy way to recalculate. But I'm getting the same numbers everyone else is: about a 25% chance to recover without help, otherwise you're pretty much guaranteed to die within 20 rounds. Average death round is about 6.5, and average recovery round (if you recover) is about 8.8.

 

[baberg]

This talk of stabilization and role/roll playing has me wondering which way would be "best" to handle the rolls - secret DM rolls or player rolls. Maybe let the PC who's bleeding out see the rolls just so he knows you're not screwing him, and to maybe add tension, but if I'm playing as a still-alive PC and know that my buddy on the floor has been rolling well, I'm going to be more anxious to end the fight quickly and then worry about healing him, instead of immediately rushing to do first aid.

This probably comes back to the whole "gamist/simist" thing again though. Simulation wise, secret DM rolls are best. Gamism wise I'd like to know exactly what the odds are that my buddy's going to bleed out next round.

 

[Revinor]

But you only fail on a 1-9.

Indeed, you are right - I have looked at the numbers given by OP instead of doublechecking in rules.

New numbers are as follows

Round 1, die 0.000000(0.000000), stabilize 0.050000(0.050000)
Round 2, die 0.000000(0.000000), stabilize 0.097500(0.047500)
Round 3, die 0.091125(0.091125), stabilize 0.142625(0.045125)
Round 4, die 0.227813(0.136688), stabilize 0.180938(0.038313)
Round 5, die 0.364500(0.136688), stabilize 0.210500(0.029563)
Round 6, die 0.478406(0.113906), stabilize 0.231750(0.021250)
Round 7, die 0.563836(0.085430), stabilize 0.246242(0.014492)
Round 8, die 0.623637(0.059801), stabilize 0.255738(0.009496)
Round 9, die 0.663504(0.039867), stabilize 0.261770(0.006031)
Round 10, die 0.689133(0.025629), stabilize 0.265506(0.003736)
Round 11, die 0.705151(0.016018), stabilize 0.267774(0.002268)
Round 12, die 0.714940(0.009789), stabilize 0.269128(0.001354)
Round 13, die 0.720813(0.005873), stabilize 0.269924(0.000797)
Round 14, die 0.724284(0.003471), stabilize 0.270387(0.000463)
Round 15, die 0.726308(0.002025), stabilize 0.270654(0.000266)
Round 16, die 0.727476(0.001168), stabilize 0.270806(0.000152)
Round 17, die 0.728143(0.000667), stabilize 0.270892(0.000086)
Round 18, die 0.728522(0.000378), stabilize 0.270940(0.000048)
Round 19, die 0.728734(0.000213), stabilize 0.270967(0.000027)
Round 20, die 0.728853(0.000119), stabilize 0.270982(0.000015)

and they are fitting the numbers you gave. Sorry for confusion.

 

[baberg]

Hrm. That's an awfully high rounding error.

5% off on only 100 trials? That's about an average rounding error to me. 100 is a very very small sample size, especially when we're dealing with pseudo-random numbers. I ran another 100 trials and that brought the total down to 27% survive.

I also did a run of the perl script above with the 19->20 correction and stopping after 10000 instead of 100, and here's the results:

36523 trials, 27.38% (10000) lived
AVG 3.8465 to stabilise, or 5.99004637484447 to die
Max Live time: 22 Max death time: 24

I'd like to do a little more, maybe make a graph of what round death occurred as I'm not convinced that simply averaging the numbers is the "right" way to look at it... but maybe it is.

 

[catsclaw]

5% off on only 100 trials? That's about an average rounding error to me. 100 is a very very small sample size, especially when we're dealing with pseudo-random numbers. I ran another 100 trials and that brought the total down to 27% survive.

Ah. I thought you ran 100 simulations, and each simulation had X trials. Which you did, I guess, if X=1.

And it's not rounding error, it's random variation. You're sampling from a potentially infinite pool, and you're only drawing 100 lots.

 

[Revinor]

I'd like to do a little more, maybe make a graph of what round death occurred as I'm not convinced that simply averaging the numbers is the "right" way to look at it... but maybe it is.

Average is very bad thing in such case. If you get 99 people earning 1 dollar per month and 1 guy earning 9901 dollars per month, average salary is 100 dollars[1]... Probably median is a lot better number to look at.


[1] - and if doctor got visit from 50 20-years old males and 50 40-years old females, his average patient is 30 years old hermaphrodite...

 

[catsclaw]

Average is very bad thing in such case. If you get 99 people earning 1 dollar per month and 1 guy earning 9901 dollars per month, average salary is 100 dollars[1]... Probably median is a lot better number to look at.

Doesn't move the numbers much. Mean round of death: 6.7. Median round of death: 6. Mean round of recovery: 8.6. Median round of recovery: 8.

Interestingly, if you exclude the trials where you die before you recover, the mean round of recovery drops to 3.8 (median 3). Once you get past that point, the number of fails you've racked up start to really hurt you.

 

[komi]

I didn't have time to read all the posts, but I wrote this up for another message board. Instead of giving the chance of dying and stabilizing, I give the chance to be alive on round x. Also, I compare with 3.5 rules:

Since we were talking about hit points, I crunched some stats on the new 4e stabilization system. Details of the system are here:
http://www.wizards.com/default.asp?x=dnd/drdd/20080201a&authentic=true

Here's the gist: Each round, roll a d20; 1-9 bleed, 10-19 nothing, 20 stable; 3 bleeds before stable is death

All the statistics assume no healing of any sort.

4e (3.5e)
(NOTE: For 3.5e, statistics depend on how negative your hit points are. So I assume this is an unknown with values -1 to -9 being equally likely. Framing it this way is less useful in practice, but it allows for a direct comparison between systems.)

Chance of dying: 72.9% (61.3%)
Expected number of rounds to die: 6.00 (4.31)

Chance of being alive after:
round 1: 100.0% (90.0%)
round 2: 100.0% (81.0%)
round 3: 90.9% (72.9%)
round 4: 77.2% (65.6%)
round 5: 63.6% (59.0%)
round 6: 52.2% (53.1%)
round 7: 43.6% (47.8%)
round 8: 37.6% (43.0%)
round 9: 33.6% (38.7%)
round 10: 31.1% (38.7%)
.
round Inf: 27.1% (38.7%)

 

[Xorn]

This is how it was presented in the Design and Development article in the "Try it now" section.

In the Scalegloom rules appendix under "Hit Points, Healing, and Dying" (p24) though, their is no mention of anything special happening on a roll of 20 on 1d20. If the rules in Scalegloom are true, it appears there is no way for an unconscious and dying PC to stabilize without the help of his friends, as far as I can see?

I think we will have to wait until June to know which is true.

I think the "stabilize on 20" idea sprouted from the normal saving throw roll:
1-9: fail
10-19: save
20: all effects saved

 

[stripes]

I'd like to do a little more, maybe make a graph of what round death occurred as I'm not convinced that simply averaging the numbers is the "right" way to look at it... but maybe it is.

Ouch! The graph shows a diffrent tale (L = live, D = dead, space = bleeding, 80chars == 100%):

                                                                           LLLL
                                                                       LLLLLLLL
DDDDDDD                                                             LLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDD                                             LLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDD                               LLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD                    LLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD              LLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD        LLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD     LLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD   LLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD  LLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD LLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLL
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDLLLLLLLLLLLLLLLLLLLLLL

So on the 3rd turn onwards you have a higher chance to be dead then to be alive and not long after that you have a higher chance to be dead then to be still bleeding.

Oh, and for anyone that wants to graph along at home:

#!/usr/bin/perl

use strict qw(vars);

my(@dead, @live);

while(@dead < 100 || @live < 100) {
    my($res, $round) = &zero_hp;
    if ($res) {
        push(@live, $round);
    } else {
        push(@dead, $round);
    }
}

my $tot = @dead + @live;
printf "$tot trials, %4.2f%% (%d) lived\n", 100 * @live / $tot, scalar(@live);
print "AVG ", &avg(@live), " to stabilise, or ", &avg(@dead), " to die\n";

print "\n" x 3;

my(%dead, %live);
foreach my $t (@dead) {
    $dead{$t}++;
}
foreach my $t (@live) {
    $live{$t}++;
}

my $W = 80;
my($dead_so_far, $live_so_far) = (0, 0);
for(my $t = 1; $t < 25; $t++) {
    $dead_so_far += $dead{$t};
    $live_so_far += $live{$t};
    my($dsf, $lsf) = ($W * $dead_so_far / $tot, $W * $live_so_far / $tot);
    print "D" x $dsf, " " x ($W - ($dsf + $lsf)), "L" x $lsf, "\n";;
}

sub avg {
    my(@n) = @_;
    my $tot = 0;

    foreach my $n (@n) {
        $tot += $n
    }

    return $tot / scalar(@n);
}

sub zero_hp {
    my $bleed = 0;
    my $rounds = 0;

    while($bleed < 3) {
        $rounds++;
        my $d20 = 1 + int(rand(20));
        if ($d20 <= 9) {
            $bleed++;
            print "$d20: BLEED ($bleed)\n";
        } elsif ($d20 <= 19) {
            print "$d20: no change\n";
        } else {
            print "$d20: STABLE!\n";
            return (1, $rounds);
        }
    }

    print "Sorry, you die (took $rounds rounds)\n";
    return (0, $rounds);
}