I have a vague memory of playing a game as a child that involved pencil & paper and, maybe, dice. The idea was that you were managing a lemonade stand, and each cycle of the game was a “day” of selling lemonade. You then had to figure out how to allocate your profits and plan for the next day, etc.
Is this ringing a bell for anyone?
I remember playing Lemonade Stand on the Apple ][.
Heres a online version for you.
Yeah, but the programmers were lazy.
If it was a 50% chance of rain, it never rained.
If it was a 30% chance of rain it always rained.
Those were the only two rain stats, and the percentages themselves were never used.
It was the first time I ever played that game (4th grade). Later incarnations/variations actually implemented real statistics.
Never heard of the OP game, but since this is the Game Room and since the title asked for a children’s game, and the OP mentions pencil & paper, one I do remember is how we killed time in church when we weren’t seeing how long we could hold our breath.
Pig in a Pen. Ring a bell for anybody? May have other names, but you made a grid-type layout of dots in a rectangle, as many as you felt would last until the sermon was over. Then you’d take turns connecting pairs of dots with lines. When your line formed the fourth side of a square you got to put your initial in that square and make another line connecting two more dots. If that line also completed a square you kept going until your line didn’t finish a square.
Tons of fun.
As best I can recall we didn’t have dice in church because they would have made too much noise, but we did like to fart as loud as we could using the pew for reverb. Good old days.
How is the pencil-and-paper version played?
Of what? Pig in a Pen? If that’s the one you mean, it’s all pencil and paper. Backs of offering envelopes and those little eraserless pencils like they use at Putt-Putt.
Yes, I remember that! It had an addictive quality, because in the end stages of the game, you’d complete long stretches of boxes.
Googling DOTS GAME turns up several online versions.
Confucius say: Man who fart in church, sit in own pew.
So glad you caught that pun-able offense. 
We call it Dots, and my boys and I often play it. We usually do a grid that’s 10x10 or so, but you can go bigger.
No, the lemonade game I mentioned.
Cool. I didn’t think you meant my sidetrack, but answered as if you had. I’ve honestly never heard of your OP game. Sorry.
Fun game. It was always great if you got the chance to make that play where you’d rack up a line of squares in a series.
We had the Apple ][e version of the Lemonade Stand game when I was a kid-- We inherited all our games from a retiring teacher, so almost everything we had was educational. There were actually three or four different games of varying complexities on the disk: In the first one, you were selling apples, and could harvest an unlimited number of apples from your tree every day, and the only variable was price (the lower the price, the more apples you sold, but the less profit you made on each). In the second one, you were selling tomato plants your class had grown as a science project, and could vary the price and also put up advertisements: The more advertisements, the more you sold, but each ad had a price. Finally, there was the lemonade stand, which incorporated all sorts of things: A weather forecast (temperature and chance of rain), road construction, costs of raw materials (at one point your mom stops giving you free sugar, so your costs go up), etc., and at the beginning of each day, you have to decide not only what price to charge and how much to advertise, but also how much lemonade to make (unsold lemonade still costs you raw materials, but goes to waste, and if you run out, you can’t sell any more).
I must have had an updated version, because I remember the chance of rain making at least some sense (when it listed a higher chance, it really did rain more often), and I’m pretty sure I also remember some days with a 5% or 95% chance.
That’s a mighty odd role playing game, the only kind of game with pencil, paper and dice I can recall playing in my youth. I wonder if GURPS would cover it?
I remember that game from second grade on an Apple II. Must have been '95 or so.