Gemara

30a (Rava): The Halachah is, we are concerned for mixed wine for exposure and Nisuch (lest a Nochri offer it to idolatry).

73b (R. Yochanan): If two cups of diluted wine, Chulin and Terumah, got mixed, we ignore the Chulin wine, and the water is Mevatel the Terumah.

74a (Mishnah): If Yayin Nesech fell into a pit (of Kosher wine), one may not benefit from all the wine;

R. Shimon ben Gamliel says, one may sell it all to a Nochri, except for the value of the Yayin Nesech.

Bava Basra 96b (Rava): All agree that if one put three measures of water on dregs and four measures of liquid come out, it is considered wine.

This is like Rava taught elsewhere, that if wine cannot be mixed with three measures of water, the wine is substandard.

(Rava): All agree that if one put in three measures and three come out, it is considered water. If he put three, and three and a half come out, Chachamim say that the same water came out, and a half-measure from the dregs. There is six times as much water as dreg-wine, so this is not wine. Others say that two and a half measures of water came out, and one from the dregs. There is two and a half times as much water as dreg-wine, so this is wine.

97a (Beraisa #1): If one puts water on dregs of Ma'aser wine, (what comes out) the first time is forbidden (like Ma'aser. The second time is permitted.) With Hekdesh dregs, the first three times are Asur, and the fourth is permitted;

R. Meir says, even the second time with Ma'aser is forbidden, and, even the fourth time with Hekdesh, i.e. (in both cases) if it tastes like wine.

Contradiction (Beraisa #2): Dregs of Hekdesh are always forbidden.

Answer: Regarding Kedushas ha'Guf (e.g. wine that is offered on the Mizbe'ach), the dregs are always forbidden. Regarding Kedushas Damim (their value is Hekdesh), only the first three times are forbidden.

Nedarim 55a: Rava was concerned lest Rav Yosef was upset with him. He told Rav Yosef's attendant 'let me mix the wine for him.' Rav Yosef tasted the wine, and said 'this is how Rava mixes wine!'

Rishonim

Rif (10a): Yayin Nesech applies to mixed wine.

Ran (DH Yayin Mazug): Some say that we are concerned for Yayin Nesech only when there are less than three parts of water for each part of wine. If it is diluted more, it is not wine and Yayin Nesech does not apply. They bring a proof from Bava Basra 96b. If three and a half measures came out, Chachamim say that only a half-measure is from the dregs, so it is not wine. Others say that one measure is from the dregs, and two and a half are water. If there were three measures of water, all would agree that it is not wine, for there is more than three times as much water as dreg-wine. This is no proof. It refers only to dreg wine. If real wine is diluted, as long as it tastes and looks like wine, Yayin Nesech applies. The Ra'avad says that Yayin Nesech is stringent, so we do not follow these Shi'urim. We say in Bava Basra that (wine made form dregs of) Hekdesh is always forbidden, for it is stringent. Likewise, Yayin Nesech is stringent like Hekdesh!

Ran (36b DH Garsinan): The case is, the two cups contain is water 60 times the amount of Terumah. We can say that the cups were mixed normally, three parts of water for each part of wine, if the Chulin cup is 19 times bigger, so it has water 57 times the amount of Terumah, and there are another three parts of water in the Terumah cup. R. Yitzchak says that the cups are equal size. In all, there are six parts of water against the Terumah. We ignore the Chulin wine, and the Terumah wine is Batel in six parts of water. Normally, Min b'Eino Mino (when mixed with another species), Terumah is Batel in 60, like other Isurim. Wine is Batel in six parts of water, for it does not improve the water. It is detrimental, i.e. Nosen Ta'am li'Fgam, which is permitted regarding all Isurim. According to this, our Mishnah forbids wine that became mixed with water when it improves it, i.e. there is at least one sixth wine. If there are more than six parts of water for each part of wine, it is li'Fgam and it is permitted. It is a mere acidity.

Note: Rav Yosef tasted wine, and remarked that Rava mixes this way. This connotes that Rava diluted wine with three parts of water, but most people did not (rather, with two parts of water, like Abaye)! Perhaps indeed most mix like Rava. Rava used to mix for Rav Yosef (the Rosh Yeshiva) to serve him. He was replaced by one who diluted with two parts. When Rav Yosef tasted the weaker wine, he recalled that Rava used to dilute it that way.

Tosfos (Zevachim 73b Sof DH Rebbi): R. Yitzchak ha'Lavan says that the cups contain water 100 times the volume of the Terumah.

Ran (37b DH Gemara): The Ra'avad holds that if enough of wine became mixed with water that it is proper to drink the mixture like wine, even in pressed circumstances, this is like wine or vinegar added to Kevashim (pickled vegetables) according to Chizkiyah, who forbids benefit (38b). We do not permit selling all but the value of the wine, for it was Machshir (improved) the Kevashim. If Stam wine of Nochrim became mixed with Kosher wine, if the Nochri wine would suffice to give taste to (all) the water (mixed with it) to be proper to drink, one may not sell it. We are stringent about mixtures of wine with wine. The Ra'avad has no proof from Kevashim. There, the Gemara teaches the law (they are forbidden). It does not discuss solutions to get some benefit from them. Perhaps one may sell them, except for the value of the wine! The Rashba brought a proof from the Yerushalmi. R. Shimon ben Gamliel admits about wine in a cooked food. This shows that if a food was improved by wine, it becomes like the wine. However, the Ra'avad added that if enough Nochri wine was mixed with Kosher wine to give taste to the water, one may not sell it. This is wrong. The Mishnah discusses (any quantities) of wines that mixed, and R. Shimon ben Gamliel permits selling except for the Yayin Nesech, and the Halachah follows him. Also, the Yerushalmi forbids selling only wine that fell into a cooked food. This implies that one may sell if wine fell into wine, even in a similar case, i.e. when there is enough Isur to improve the Heter.

Rambam (Hilchos Ma'achalos Asuros 11:9): Only wine Kosher for the Mizbe'ach is poured to idolatry.If a Nochri touched mixed wine, it is forbidden.

Rambam (16:30): If water became mixed with wine or vice-versa, it is b'Nosen Ta'am, for this is Min b'Eino Mino.

Rosh (Avodah Zarah 2:13): Yayin Nesech applies to mixed wine as long as it tastes like wine. Regarding dregs, we distinguish between when three measures come out, and when three and a half come out, regarding Borei Peri ha'Gefen. That is because a mere acidity comes out of dregs, even if it has the taste of wine. People dilute pure wine according to their nature and custom. Therefore, Yayin Nesech applies as long as it tastes like wine.

Tosfos (Chulin 25b DH ha'Metamed): Why do Chachamim exempt (from tithes) dreg wine with the taste of wine (when three and a half came out)? For every Isur Torah, Min b'Eino Mino the Shi'ur is b'Nosen Ta'am! Tevel is more stringent about Eino Mino! One opinion says that Chachamim exempt even if it fermented, even regarding Vadai Tevel! We can say that when wine is mixed with water, even if there are less than 60 times as much water, even if he three and a half came out, it is not a proper taste of wine. It is a mere acidity.

Poskim

Rema (YD 123:8): If mixed wine has the taste of wine, it is forbidden if a Nochri touches it. Some permit if there are six parts of water.

Beis Yosef (DH Yayin): The Rashba wrote the reasonings of the opinion in the Ran (that more than three parts of water for each part of wine is not wine) and the Rosh (that it depends only on whether it tastes like wine), then cites Chachamim who say that even if wine of Nochrim falls into six parts of water, the taste is annulled (so it is permitted).

Shulchan Aruch (134:5): If (a Nochri touched wine, and it became mixed with) six parts of water for each part of wine, this is enough to be Mevatel the taste of wine, and one may drink it.

Taz (5): Some say that this is because wine can be diluted with three parts of water, so in six parts it is Batel in the majority. This is wrong. The weakest wine can be diluted with three parts of water, but stronger wines can be diluted more than this! Rather, the Gemara says that wine is Batel in six parts of water, so we may not be lenient for anything less.

Rema: If there is less water than this, he sells all of it to a Nochri, but does not take the value of the Yayin Nesech.

Beis Yosef (DH v'Yayin, citing the Rashba): If Yayin Nesech gives taste to water, some say that one may not sell any to a Nochri. The wine is Machshir the water, so the water is like the Ikar (wine). My Rebbeyim permit to sell, except for the value of the Yayin Nesech. This is primary.