Ok. So a kid has a 2 in 20 (essentially 1 in 10) chance of dying each year.
They have to roll said check once a year for 15 years.

What then are the odds, rolling 2/20 for 15 times, that your child will die at some point in those 15 years?

How many children would you have to have in order to reasonably expect that at least one of them would live to adulthood?

RPGPundit

18 * 15 = 270
20 * 15 = 300

270 / 300 = 90 %
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I´d say you have a ten percent chance that your child lives to see his 15th birthday.
Any math guru shall gleefully correct me.

Actualy it's a bit better than that.
 
Age v.s. survival
0  Congradulations kid, you survived childbirth. Survival = 1.00
1  9/10 of children make this roll. Survival = 0.9
2  of those, only 9/10ths survive. Survival = 0.81
3  (9/10)^3 = Survival 0.73
4  0.66
5  0.59
6  0.53
7  0.47
8  0.43
9  0.38
10  0.35
11  0.31
12  0.28
13  0.25
14  0.23
15  0.21 survive
So roughly one in five kids survive to the ripe old age of 15.

Number of babies v.s. odds of getting at least one 15 year old
1  0.21
2  0.37
3  0.50
4  0.60
5  0.68
6  0.75
7  0.80
8  0.84
9  0.88
10  0.90
11  0.91
12  0.94

So if you want to be 90% sure to have at least one surviving child, either have ten babies OR have one 14 year old.

If you're ok with 50/50 odds, either have three kids or have one seven year old. [/gleeful correction]

Or if you're not showing off

it's just .9 to the power of the year: .9 ^ Year

It should probably be stressed that the chances of your kid dying - just as in the real medieval era - are strongly dependent on your circumstances. If you're not going to better yourself and provide for your family, of course your kids will be sickly.

In my experience, most Pendragon characters fairly soon start earning enough money to live well enough to eliminate the chance of child death.

Quote from: WarthurIn my experience, most Pendragon characters fairly soon start earning enough money to live well enough to eliminate the chance of child death.

Or at least minimise it.  It's rather neat how this dynamic has been built into the game to provide character motivation to go forth and be great.  Of course, it also creates the dynamic where the temptation to be a vicious brute in order to support your family runs headlong into your chivalric and religious virtues -- another neat aspect of the mechanics.

!i!

(P.S. Siring lots of bastards helps up the odds of genetic continuity, too.  Granted, they can't be your legal heir, but at least you can guarantee a follow-up character if your proper lineage falls on hard times.)