In Scotland and the North of England, wadd was a term used by children for a penalty paid upon losing a game. This appears in many, many games, and I suspect that these were often an add-on to make childish games more interesting to older kids -- particularly those in their teens. The game of 'tig and wadds' ('tag and forfeits'), for example, clearly shows a childish game updated for edgy teens. Because, as it turns out, wadds were very much the same sort of thing a hundred years ago as they are today.
"The {person playing it} says to the one in the wadd, 'Whether will ye hae three questions and two commands, or three commands and two questions to answer, or gang on wi’, sae that ye may win out o’ the wadd?'" 1
Which is to say, truth or dare, except you'll have two of each either way, you just get to pick the fifth. These were sometimes quite childish ("kiss the crook"2) and sometimes quite teenagery-ish ("beg for a kiss"3). An example of a 'Truth' was "Suppose you were in a bed with Maggie Lowden and Jennie Logan, your twa great sweethearts, what ane o’m wad ye ding owre the bedside, and what ane wad ye turn to and clap and cuddle?" Or consider:
"Suppose ye were in a boat wi’ Tibbie Tait, Mary Kairnie, Sally Snadrap, and Kate o’ Minnieive, and it was to coup wi’ ye, what ane o’ ’em wad ye sink? what ane wad ye soom? wha wad ye bring to lan’? and wha wad ye marry?"
Which is to say, a slightly confusing version of kiss, marry, kill. A lot of the wadds were questions about who you liked or didn't, and the remainder are chances to embarrass the looser. It's quite likely that in most cases the wadds took longer than the game, probably by a good bit. There was, in fact, a game simply called 'Wadds' that is just a structured chance to ask members of the opposite sex who they like.4 In Wadds, one person sings that they must go home, a member of the opposite sex presents one of their friends as a companion for the journey, and the appropriate acceptance or refusal verse is given in reply. If a refusal is given, a wadd is given in the form of a small token (a penknife, a ribbon, a bit of money). The game ends with all those who gave a wadd earning it back by completing a small dare -- kiss the one they refused, kneel to the prettiest in the room, or bow to the wittiest, etc.
The word probably comes from Wadmal (sometimes shortened to wad or wadd-cloth), which was a rough woolen fabric that was historically used as a form of money or to indicate a pledge in Nordic counties and down into Scotland. It may, alternatively, come more directly from the Old Norse veðja, meaning 'to bet', the same root that gives us the Swedish vad and the Norwegian vedde.
Footnotes:
1. The examples above come from the book The Traditional Games Of England, Scotland, and Ireland, collected and annotated by Alice Bertha Gomme (pub. David Nutt, London, 1898).
2. The hook a cooking pot hangs from. Because it's all sooty and disgusting, that's why.
3. The example given was that one would have to stand in a corner and recite a rhyme requesting a kiss (“Here stan’ I, as stiff’s a stake, / Wha ’ill kiss me for pity’s sake?”) until someone does so.
4. There were actually lots of games like this, including Biggar and Hey Wullie Wine, most of which included a wadd of some sort.