Last I saw in a chess book, around 55% of the time results favour White (i.e. White wins, with the [half-]value of White draws factored in, too), for any kind of a monster size database (though ratings could be low, besides high ratings, for all of the players involved).

Whether a (FIDE) chess player of any strength that is participating in a chess event (of any kind) decides to try to play for a win or a draw may depend on one or more factors, such as their desire to gain/risk rating points of whatever kind (or if possible cash prize $ are taken into account, especially if a game is being played towards the end of such an event).

Such factors are regularly taken into account even when contemplating what to possibly play (if allowed, perhaps anticipating a position that might arise well into the move/turn count) right from the setup position in a given chess game. If a player knows well enough in advance that they are to be paired against someone, they might look over any available previous game(s) that that future opponent has played vs. anyone (such as in a large database, similar as for anyone who plays on Game Courier on this CVP website might choose to research other players' previously played games in the GC Database - more worth the effort, perhaps, if their and their opponent's GC ratings are fairly close in value).

A situation that is more of real concern at elite players levels (the worst cases regarding extreme difficulty, in trying to win in a given game, even with either colored chess army, occur in high level correspondence chess play, or in high level computer engine matches, even, for a number of years now - the percentage of draws in such cases are downright depressing, to me personally - fortunately these two cases are of little interest to chess promoters, or to chess fans in general) is that winning in a game of chess when starting out with the Black army, even if Black may be able to thoroughly prepare for a given opponent in advance, is if Black is none too sure that White won't try to steer for a drawish/dull/solid position possibly right from the setup (or, to some extent, even if Black knows that that sort of approach by the player to play White will be his intended strategy).

Then, it may be that if Black needs to win at all costs, he may well be advised to hope to get to play a (at least) somewhat risky chess opening (even if it's a well-tested defense, say against 1.e4 with Black), or try to, e.g. grind down (i.e. play on against, for many, many moves as long as needed/[reasonably justifiable] vs.) a player of the White pieces if he plays quite unambitiously, but still sufficiently solidly (for example), i.e. by adequately avoiding a sharp tactical opening that Black may have hoped for. In such a case, e.g. in a high level chess chess match, it can be like in a boxing match where wearing down an opponent (i.e., as if to try to eventually induce him to make mistake[s] that prove to be too costly to him, before a position happens to be reached in the game where a drawn result more or less cannot be avoided), say by having greater stamina, may prove successful at least some of the time.

If I recall right, even the late Bobby Fischer may have had at least sometimes tried that approach in a given FIDE chess game of his, at least very long ago, in his younger days (these days, elite players may have a bit too much respect for each other's skills, as I somewhere read words to that effect, some years back - I also recall at the least one world chess championship, not too many years ago, had all 8 games at slow time controls drawn, when by the match rules, the players then resorted to playing games in a tiebreaker phase, with faster time controls - Magnus Carlsen won that particular match [among others, a number of years back], though he was significantly younger then, when as his match strategy he concentrated on trying to play cautiously, just so as to get past the first 8 games, to try to win with his quick thinking/reflexes in the tiebreak phase - there are too few slow time control games with that sort of format for a world chess championship match, for my liking, and I'm unsure if Magnus' opponent tried to take much risk in playing in the opening stages of those 8 games, even when playing in his 4 games with the White army).

Anyway, whatever strata is chosen to define what is an elite (or ultra-elite!?) level (such as for chess itself), as you have alluded to such a level is something that most of us can only dream of reaching, but at least before reaching such a level, we have less problems in winning our games, percentage-wise, rather than our having what might be perceived as too many draws (most especially with Black). So, possibly having great difficulty, on a somewhat regular basis, in trying to win (with either army) is not such an issue for us, unless, e.g., we worry a bit too much about whether our chess opening repertoires (as if they were never to change very much, in our own 'chess career') could in theory help us to win as needed if we ever were to reach such an elite level.