If it’s always two players to a game, why not a system where heads is always Player 1 and tails is always Player 2? (Or vice versa.)
That being said, if there is a table nearby, I’d actually recommend using dice over coins. Assuming the die has an even number of faces, designate evens as heads and odds as tails. I’ve been in events where people have taught themselves how to manipulate coin flips to land a certain way more often, to where coins were eventually banned as a way to decide things. While it can be done, it’s harder to manipulate the outcome of a roll of dice.
(Don’t use rock-paper-scissors though. Even I know how to play rock-paper-scissors to guarantee at least a 70% win rate.)
It is generally quite advantageous to be the last player in a game, since on your last ball you know exactly what score(s) you need to beat. This advises you as to how aggressive you should be with nudging, how important it is to set up a huge (risky) stack vs. taking smaller easy points, and so on. It does require a reasonable depth of knowledge on the specific game you’re playing; for example, you need to be keenly aware of how much bonus you have at any given time, and whether that amount of bonus is enough to earn you the match points you need. At some point it may make sense to transition to feather-flipping, to ensure that you don’t tilt. (Note: in tournament play, often, winning isn’t the goal! For example, you need to be aware if simply surpassing one other player is good enough, given the match-point situation coming into the current game. If getting one more match point will advance you to the next round, you will probably want to focus exactly on getting that one match point, which means targeting the next player ahead of you and ignoring everyone else.)
And even on balls other than the last one, if you’re the last player, you’ll have a sense of what your opponents are planning before you have to step up to the machine. Even on ball 1: Are your opponents setting up the Big Ultra Mega Stack (big risk, big reward) or are they chipping away at smaller easier points? If you’re well-acquainted with the game, this is very useful information.
Playing last has all of the advantages stated. The most common reason players sometimes opt to go first is game-state asymmetry. This occurs when, for instance, a ball is already locked at the start of the game and can be released by player 1 [Fireball]; where a variable-value feature in the game will start the game for player 1 at its maximum value [some EMs’ spinners or saucers]; where balls locked by a player ahead of you result in, when you earn a lock, not a fresh ball being kicked out into the plunger lane but a ball kicked onto the playfield in a way that’s riskier or less shot-convenient than the plunger lane; or where you can do something lock- or other-wise that earns you a higher value than a player doing so later. Even in these cases, though, the asymmetry advantages are not always large enough to overcome the strategic advantage of going last.
Other reasons players sometimes go first (or not-last) are hoped-for intimidation (put up a big ball one and hope that the pressure that puts on the other players hurts their effectiveness), “icing” later players via delaying when they will start, playing at least ball one without the pressure of knowing that someone actually did put up a big number ahead of you, and forcing yourself to try to maximize your score rather than shoot for a specific point target.
Then there’s the “if you choose the game, you’ll probably have to go first issue.” If you’re relatively indifferent about which game gets played, you might choose to go last and let someone else pick game. If game choice is more important to you, you take that over position. You’ll see players at all levels doing each at one time or another.
I can guarantee you that it is not so intense in pinball tournaments that people are manipulating the coin toss so that they get an advantage. That’s really just not happening. People ro-sham-bo too if they want. As you said, it can be easy to anticipate the other person’s choice, but then so can they. It’s super universal. And we’re talking about the choice to jockey for position. You still have to play the best game possible. Seriously, no one is trying to cheat a coin toss.
Yeah, I played in a tourney last week and it took all my concentration to simply flip the coin without dropping it (my sobriety level had a lot to do with this). Plus, generally the other person calls it while the coin is in mid-air. I don’t think people can regularly manipulate the coin after that point. But anyway, manipulating tosses simply isn’t an issue.
To even reiterate this point, I’ve had so, so, so many people “win” the coin toss and be so indifferent about going first or second. “I don’t care, whatever you want to do.” Why the hell did we flip then? Just make a choice. Usually they then pick to go first. I like going last just to see their strategy, bounces, and what points I need to make up if any. Also, I gotta admit, it feels pretty bad a$$ to have a walk off win on ball three where you just plunge, shake hands, and walk away.
@kayluh touched on another great reason to play last: to have a chance to examine the machine and see how it’s playing. Is the slot machine kickout on TZ nicely drop-catchable / bounce-passable, or do you have to worry about it trying to go down the middle? If you shoot around an orbit, will the ball strike the top of the slingshot and bounce somewhere evil (like the opposite outlane) or will it glide smoothly to the flipper? How sensitive is the tilt?
If you’ve been playing the same machines round after round in a tournament, you may already have these answers. In a situation like Pinburgh, where you’ll typically play 40 distinct machines, it can be very helpful to play as late as possible and watch while others are playing to see what’s what. (Of course, make sure you’re not getting in the player’s line of sight or otherwise interfering with them!)
I personally prefer to go first unless there is something like carryover ball locks. This is mostly on machines I play all the time though so no need to really see how a bounce, kickout, or tilt is set. The reasoning I have is that I’m going to force the other player to beat me so pressure is on them.
I chose first on Doctor Who tonight at league (becuase I had the choice after getting totally hammered on Indy 500) and immediately plugged the locks to take them out of play for the others. It worked, I played multiball and all the first wave video modes on ball three and managed 70 something loops… and still finished second to @kdeangelo who had over 2B.