"You went first last time." Anyone who plays games with the same person will have heard it. Sometimes it is a fair complaint. Sometimes going first is no help at all, or even a disadvantage.
For several of the turn-based games on TwoSide, the question has a known answer. Here is what is known, what is not, and what to do about it.
Two meanings of "advantage"
There is the advantage in theory and the advantage at your kitchen table.
In theory, a game with no luck and no hidden information has a fixed result if both players play perfectly: a win for the first player, a win for the second, or a draw. Mathematicians and computers have worked this out for some games.
At the table, nobody plays perfectly. A theoretical win that needs fifty exact moves is worth very little to a person. What matters is whether the first move helps ordinary players.
Keep both in mind.
Games where the first player wins in theory
Last Stone. With rows of three, five and seven, the first player can force a win by taking one stone and then keeping the position balanced. This is one of the few games where the theory is simple enough to use. If one of you knows the method, going first decides it.
Poison Square. The first player can always win, by a famous argument that proves it without saying how. No person knows the full winning plan for our five by seven bar, so in practice it hardly matters.
Five in a Row. The plain version of this game, with no extra rules, is a known win for the first player on the full-size board used in competition. A computer scientist, Victor Allis, showed that in the 1990s. Our board is smaller, eleven by eleven, and we have not seen a proof for that size, but the first move is certainly a help. Serious competitions add special opening rules to cancel it out.
Seed Pits. The standard version, six pits and four seeds, was analysed by computer around the year 2000 and found to be a first-player win. Between people it is a small edge: the first move can earn an immediate extra turn.
Games that seem balanced
Dots and Boxes. Computer analysis of small boards has reported that the sixteen-square game, the size we use, ends level with perfect play. For human players, the result depends far more on who understands chains than on who starts.
Block Out and Paint Battle. We do not know of a published solution for these exact boards. From playing them, neither side seems to have a decisive edge.
Games where luck drowns it out
Greedy Dice. Going first is a slight advantage in a race game, simply because you get the first chance to score. Over a match to fifty, the dice matter far more.
Pairs Duel. Going first is, if anything, a small disadvantage. The first player turns over two cards knowing nothing, and shows them to the opponent for free.
Sea Search. The first searcher gets one more chance if the hunt goes the distance. With three treasures in twenty-five squares, luck is the bigger factor.
What the site does
Several of the games choose the starting player at random. Last Stone, Poison Square, Block Out and Greedy Dice all do this, so that neither of you can claim the first move by habit.
Where a game does not choose for you, sort it out between yourselves.
Four fair ways to decide
Alternate. The simplest. Whoever went second last time goes first now.
Play in pairs. Play two games, each starting once. If you win one each, the match is a draw, or you compare margins: who captured more squares, or more seeds.
Loser starts. A light handicap that keeps a one-sided rivalry closer.
The pie rule. This is the cleverest. One player makes the first move. The other then chooses: keep it and play second, or swap sides and take that first move as their own.
It is the same idea as "I cut the cake, you choose the slice". The first player has every reason to make an opening move that is neither too strong nor too weak. The pie rule works well in Five in a Row. Let the first player place the opening piece, perhaps away from the centre, and let the second decide which side to be.
Settle it with a game
If you cannot agree who starts, use one of the quick games as the decider. Throw Down is rock, paper, scissors with hidden picks, first to three. Quick Draw takes even less time. Winner chooses.
The long view
The scoreboard at the top of the page counts wins across every game and every session. Over twenty or thirty matches with alternating starts, any first-move advantage washes out.
That is the best answer to "you went first last time". Do not argue about one game. Play enough of them that it stops mattering.
It is also what we like about two-player HTML5 games on a shared screen. The opponent is across the table, the next game is one tap away, and the rivalry is the thing.