Say the game is tied in the bottom of the 9th, you have a runner on third and one out, what is the best strategy for scoring a run and winning the game? Is it a play that requires the current batter to sacrifice himself, or is that risky since you're then down to only having one batter left? Should the batter bunt it, or only bunt it when the strike count is at 2?
There are five basic strategies when there is a runner on 3rd and less than 2 outs (1-0 doesn't matter much). Provided its a tie game or you are down by one.
The riskiest is the suicide squeeze. This is a decent percentage play, but comes with a good amount of risk. The batter bunts the ball and as the ball is pitched the runner on third breaks for the plate. The batter must get the bat on the ball or the play becomes a straight steal of home which requires a good bit of luck (or panache on the part of the runner) to pull off.
Similar to the first, the safety squeeze is another option. This play is very similar to the squeeze bunt, but the runner waits until the batter has the bunt down to commit to going home. If the opposing team elects to go to first with the ball, the runner is usually safe, but if the fielder goes home, it's a much lower percentage play than a squeeze with a successful bunt. In general squeeze plays are desperate attempts when there is no other hope (generally a terrible batter is up). Article here goes more in depth.
The most conventional option here is the sacrifice fly. In this play the batter attempts to hit a fly ball deep enough to score the runner from third (the runner is allowed to tag the base and advance if the ball is caught and there aren't 3 outs). The problem here is that trying to hit a sac fly isn't actually something hitters have much control over.
For a lot of hitters, hitting a deep fly ball isn't a great option (they just don't have the power or that's simply not their game). In this case, a sharp grounder to the right side of the infield may lead to the run that they need. Usually when there is a runner on third and the game is very close, the infield will play in on the grass, this provides them with ample opportunity to throw the ball home, but leaves them susceptible to well hit grounders getting through to the outfield scoring hte runner. Again, this isn't necessarily something hitters have a huge amount of control over.
The last option is actually the best in a late and close situation if you are down a run. That is simply to change nothing about your approach. Here's the thing, if there are fewer than 2 outs, there is a runner on third, just simply taking a normal approach leaves you with a run expectancy of between 1.43 (0 out), and .989 (1 out). The odds of scoring a single run are between 85% (1 out) and 67%.
So from the fact that squeezes are high risk, relatively low reward (back yourself out of a potential big inning or worse any run scoring situation at all) and the fact that how you hit the ball is something of a crapshoot, the absolute best thing you can do is...rely on your hitters to do their jobs.
The truth is, with an average ML hitter at bat (or even any hitter above replacement level one to be honest), your best bet is actually to just let them bat. You'll score about 1 run per inning in a situation with a runner on third and 1 out. That's not a guarantee, but that's probably about as close as you come in baseball.