11/15/2011 08:06 am ET Updated Jan 21, 2012

The Single Child Equation: When Parents Just Aren't Enough Fun

Wanted: One child, part-time only, flexible hours. Ages 5-7, girl preferred, though boys who like American Girl doll play will be considered. Must be available for play dates, excursions, dinner with grown-ups. Sleep-over expertise desirable. All snack, outing, and transportation expenses covered; no reciprocation required.

If there was such a thing as "Craig's List for Parents of Only Children," that would be my ad.
You will notice that I am not actually seeking a second, just a loaner, a child we would happily return to her rightful family as needed. In the music world, she would be called a "ringer": someone who fills in whenever an orchestra wishes; though this performer's talents are much appreciated at show time, she is meant to pack her violin and move along afterward.

We need a ringer because, as our only child gets older, it has become clear to her that two 40-something men are not as consistently fun as kids her own age. This wasn't always an issue: When she was a baby, I strapped her on and took her everywhere for stimulation --sing-a-longs, parks, the local mom's group. When she was a preschooler, we spent most of our time with dear friends whose kids she'd known since babyhood. But when they moved away, it became painfully obvious how much their children had acted as proxy siblings for our gal.

It's not like she can't get one dad or the other to sit on the floor and enact elaborate serial dramas involving Barbie talent shows. But there comes a point when pretend-play fatigue sets in. And we adults reach that point long before she does. The truth is that I have about an hour limit on voicing the emotional dilemmas of dolls of any kind (not to mention their assorted dogs, cats, and horses). My husband is not much better, which leads us to a math problem: The Single Child Equation.

It goes like this: our daughter, now 6, would like it if the ratio of waking Hours Per Day (HPD) was nearly one-to-one with the available units of Thrill Per Parent (TPP). Yet, somehow, the HPD always exceeds the TPP, no matter how much we supplement doll play time with reading, coloring, or Scooter-riding.

In many families with children of similar age, TPP is just a bonus, something added on to Sibling Play Time (SPT). If you have two or more children remotely close in age, the math works in your favor: their HPD is divided by SPT, which reduces the remaining number enough that a very small TPP suffices. My brother and I rarely played together as children, which disproves that claim a little, but we always knew that, in a pinch, there was a built-in playmate to rely on. For my daughter, there is no similar fallback under 40 in the house.

That's why we work overtime to arrange play dates. The bad news/good news is that she is an incredibly social child, who has plenty of friends at school. The trick is wading through the thicket of scheduling that defines our parenting moment. Most of the kids have enrichment classes and many are in after-school programs; their weekends are eaten up by wee sports leagues, church, temple, Chinese school, or [fill in the blank, as parents do]. We often end up arranging play dates a week or more in advance, so that we don't miss our window. That's right, we now schedule casual afternoons of costume dress-up or monkey bar play the way we used to book a table at a hot restaurant.

We've also started factoring in an add-on child for all things possible: not just another plate at our table some nights, but an extra car seat for a trip to the mall, a fourth ticket to the Big Apple Circus, and, when she's older, one more bed on vacation. Call it the Only Child Tax, if you will. We don't mind ponying up for her to share these experiences with someone her own age, because we (too late) have come to understand how it can make a difference. We don't need her pals' parents to pay us back or return the favor, because the presence of their child is a gift to us and our daughter alike.

Not having the round-the-clock emotional and fiscal burden of multiple children, we're quite content to make room in our family fun for Someone Else's Kid (SEK). This brings me to my daughter's ideal formula, which factors in her dads but includes an outside addition. My daughter's favorite days look a lot like this: HPD = TPP + SEK. And that's not surprising: for an only child, the perfect number is always plus-one.