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Flesh to Stone states:

You attempt to turn one creature that you can see within range into stone. If the target's body is made of flesh, the creature must make a Constitution saving throw. On a failed save, it is restrained as its flesh begins to harden. On a successful save, the creature isn't affected.

A creature restrained by this spell must make another Constitution saving throw at the end of each of its turns. If it successfully saves against this spell three times, the spell ends. If it fails its saves three times, it is turned to stone and subjected to the petrified condition for the duration.

My reading of this is that the initial save against the spell counts as one of the failed saves so if the target failed an additional two saves it would be petrified. Is this correct or is the correct interpretation that the target must fail three of the subsequent saves to be petrified?

the spell Contagion uses a similar mechanic but has slightly different wording that makes it clear the first save is not counted.

At the end of each of the poisoned target's turns, the target must make a Constitution saving throw. If the target succeeds on three of these saves, it is no longer poisoned, and the spell ends. If the target fails three of these saves, the target is no longer poisoned...

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That is correct, the initial failed save counts as the first.

The rules say "If it fails its saves three times" not, "If it fails its saves a further three times". The sentence isn't particularly ambiguous, failing the saving throw for this spell three times makes it take effect.

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    \$\begingroup\$ "If it fails its saves three times" is not ambiguous in and of itself. What is ambiguous is whether 'its saves' refer to all saves, including the initial one, or just the another Constitution save at the end of each of its turns. The spell creates two different classes of saves. By then using 'its saves' without specifying whether that applies to all saves, or just the second kind, it is ambiguous. \$\endgroup\$
    – Kirt
    Commented Sep 24, 2020 at 20:50
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    \$\begingroup\$ This also stacks the odds in favor of failing. It means that the creature/player must make 3 successful save before they make 2 failing saves. And the reverse does not translate because if you pass your first saving throw, then you don't need to make any more; it's over! \$\endgroup\$
    – MivaScott
    Commented Sep 25, 2020 at 0:44
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    \$\begingroup\$ @MivaScott The overall chance of being petrified remains below the chance of failing a single save if you include the chance of saving on the initial saving throw. desmos.com/calculator/qloay1lrwi \$\endgroup\$
    – user60913
    Commented Sep 25, 2020 at 4:10
  • \$\begingroup\$ The difference in petrifaction between counting the initial saving throw vs not is between 2-10%. If the initial failure is a given then when it is not counted the chance of petrifaction increases by up to 14% (93% chance to be petrified with a fail rate of 76%). When the first save is counted then the petrifaction chance increases by up to 22% (86% to be petrified with a failure rate of 64%). desmos.com/calculator/pnhorrmcsc \$\endgroup\$
    – user60913
    Commented Sep 25, 2020 at 4:38
  • \$\begingroup\$ I'm just using simple math. If the first saving throw is counted, and it is a failure, then the creature must make three successes before making two failures. That seems to favor failure. On the other hand, if the first saving throw is counted, and it is a success, there is a 0% chance of petrifaction because the spell ends. \$\endgroup\$
    – MivaScott
    Commented Sep 25, 2020 at 6:22
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Based on how the paragraph is written, I would say the first failure does not count.

Let's break it down:

A creature restrained by this spell must make another Constitution saving throw at the end of each of its turns.

This only affects creatures restrained by the spell. So it is implied that there has been one failed save.

If it successfully saves against this spell three times, the spell ends. If it fails its saves three times, it is turned to stone and subjected to the petrified condition for the duration.

The creature must now make three successful saves to break out of the restraint/spell. The wording is, "If it successfully saves against this spell three times". It then uses the same wording, "If it fails its saves three times," with regards to failing saves. This would imply that the initial failure is no longer a concern. This condition wouldn't even matter if they passed the initial save.

If the first failure counted, then the phrase would have been "If it fails its save twice more", or something to that effect. The key being "more"; a reference to the earlier failure. Lacking any reference, both implied or directly, would seem to indicate that the creature is starting from zero.

Also keep in mind, that this is the same mechanism as death saving throws and the Contagion spell; best 3 out of 5.

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    \$\begingroup\$ It seems to me that the wording allows for a creature to "loop out" after succeeding at the first save. Failing the first save seems to establish loop. That would mean the creature always start the "best of five" series with one strike against it. \$\endgroup\$
    – Rykara
    Commented Sep 25, 2020 at 1:24
  • \$\begingroup\$ @Rykara Yes, and that would be weird, so probably isn't what they meant. If you get hit by it, you probably start a normal best-of-5. \$\endgroup\$
    – Owen Reynolds
    Commented Sep 25, 2020 at 3:07
  • \$\begingroup\$ @Rykara which is what this answer seems to suggest. I think once the initial saving throw is done, then you start the loop of best 3 out of 5. \$\endgroup\$
    – MivaScott
    Commented Sep 25, 2020 at 6:25

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