After all three teams lost Wednesday, the New York Mets, St. Louis Cardinals and San Francisco Giants remain locked in a three-way tie for the National League’s two wild-card slots. Our prediction model, which is based on a simulation that uses each team’s Elo rating, gives New York a 75 percent chance of grabbing at least one of those two slots, with St. Louis at 62 percent and San Francisco at 59 percent.1There’s also a slim chance — 4 percent — that either the Pirates or the Marlins sneaks into a wild card. But what are the odds all three end up tied after the final game of the regular season, thereby triggering a crazy three-game sprint to the Division Series?Elo assigns a 3 percent chance that the Cardinals, Mets and Giants have the same record on Oct. 2. However, it also projects that there’s a 0.5 percent chance a three-way tie could include the Pirates, Marlins, Rockies or even the Dodgers, if San Francisco somehow chases them down for the NL West title. Add it all up, and there’s about a 3.5 percent chance of a three-way tie in the NL.What might surprise you is that, although the NL has three teams tied right now, the odds of a three-way tie in the AL are almost double those of a tie in the NL. The AL’s possibilities are more varied; most include some combination of Toronto, Baltimore, Houston and Detroit, with other, more exotic combos that also involve the Mariners, the Yankees and even division leaders such as the Red Sox and Indians (if they botch the season’s final week and a half). No single AL trio is more likely than the NL’s Cardinals/Mets/Giants combo — the AL’s most likely is Baltimore/Houston/Toronto with a 1.1 percent chance of occurring — but because there are more viable contenders, the sum of all the various permutations comes out to a 6.2 percent probability of some three-team tie happening.In any event, today’s odds of 3.5 percent in the NL and 6.2 percent in the AL imply a 9.6 percent chance that we’ll see a three-way tie somewhere.2Multiplying 96.5 percent by 93.8 percent — the respective chance of each league not having a three-way tie — and subtracting the result from 100 percent yields 9.6 percent. There’s also a 0.2 percent chance that both leagues will have three-way ties. If we do, MLB’s tiebreaking rules are going to be a treat for those who love geeking out over strategies and hypotheticals.Say Mets/Cardinals/Giants does happen in the NL. In that case, the Cardinals would have top priority among the three (because of their superior intradivision record over the Mets and head-to-head-record over the Giants) and host a game for one of the wild-card slots. But the fun really begins in determining their opponent. The Mets have the next-highest priority, and they could choose to play on the road against St. Louis and, if they lose, play on the road again versus San Francisco in the next tiebreaker. Or they could let the Giants travel to St. Louis for the first tiebreaker game, then face the loser in a do-or-die contest at home.As Jayson Stark wrote Thursday morning, no team has chosen to slice its tiebreaker chances in half by taking the single-home-game option instead of having two cracks at it on the road, if necessary.3New York wouldn’t need the second try if it won the first tiebreaker against St. Louis. The Mets’ injury-riddled staff is in such shambles, however, that the team might ponder it. Elo would give New York a 73 percent chance of winning at least one of two road games against the Cardinals and Giants with top two starters Noah Syndergaard and Steven Matz4Assuming Matz is available after an injury knocked him out in late August. This calculation also is based on the assumption that the Cardinals and Giants trot out a starter as good as the average of their respective rotations for these tiebreaker games. on the mound — if it can manage to set its rotation enough for that 1-2 punch — compared with only a 55 percent chance with Syndergaard starting one game at home. But burning through two starters could leave the Mets with a subpar starter on the hill — and as low as a 45 percent chance of winning the wildcard game.5Assuming the Mets use their worst starter, Robert Gsellman, against St. Louis or San Francisco. Compelling, but probably not enough to justify giving up the 18 percentage point difference between having two tiebreaker chances6Again, if necessary. and just one.Of course, that’s all assuming the 3.5 percent chance of a three-way tie even becomes a reality. A two-way tie is far more in the realm of possibility — 30 percent likely in the AL, and 22 percent in the NL — but right now it’s only about 50-507Based on a 36 percent chance of some tiebreaker in the AL and 25.3 percent chance in the NL, there’s a 47.8 percent chance that neither league produces a tie to be broken with an extra game and a 7.9 percent chance that things get really wild and both teams need at least one extra game (using the same kind of calculation we used for the chance that neither league has a tie.) that we’ll see any tiebreaker at all, despite how the standings look currently. Still, that’s a lot higher than the 1.4 percent chance of one before the season.