Gemara

63b (Rav Nachman): If Reuven borrowed money from Shimon and he received more than he was supposed to, if it is an amount that could be a mistake, he must return it. If it is more than that, Shimon intended it to be a gift.

Question: What is an amount that could be a mistake?

Answer (Rav Acha brei d'Rav Yosef): (People usually count ten or five at a time.) If the error is ten(s) or five(s), he may have erred in counting a group of ten or five. If not, it is surely an intentional gift.

Question (Rav Acha brei d'Rava): If Shimon never gives gifts, what is the law?

Answer (Rav Ashi): We assume that he stole from Reuven, and wants to return the money.

(Beraisa): If one stole money and returned it by giving too much money in a subsequent transaction with the victim, he fulfilled returning it.

Question (Rav Acha brei d'Rava): If Shimon came from abroad and had no previous dealings with Reuven, what is the law?

Answer (Rav Ashi): We assume that someone else stole from Reuven, and asked Shimon to return the money in this way.

Rishonim

Rif: If Reuven borrowed money from Shimon and he received more than he was supposed to, if it is an amount that could be a mistake, he must return it. E.g. if there were five or 10 too many, perhaps Shimon counted five or 10 at a time, and erred by one. Alternatively, perhaps he made Simanim (a coin to tally each five counted), and the Siman became mixed in. Also this is an error. Anything else he may keep. If it is more than that, Shimon intended it to be a gift.

Nimukei Yosef (DH Omar Rav): Likewise, if the excess was several 10's or fives, we assume that it was a mistake. This is when people normally count 10's or fives, but not two or three at a time and to put a Siman of how many were counted. If Shimon does not give gifts, we assume that he stole from Reuven a long time ago and Reuven is unaware, and now Shimon wants to repent.

Rambam (Hilchos Malveh 4:10): If Shimon lent to Reuven and Reuven found extra, or Shimon paid his debt to Reuven and Reuven found extra, if it is an amount that could be a mistake, he must return it. If not it is a gift, or Shimon had stolen from him and include it with the loan, or someone else commanded Shimon to include it.

Magid Mishneh: The Rambam's text said 'one who lent coins and found extra', i.e. when the loan was repaid. Some texts say 'one who borrowed coins.' According to this, this is only when the borrower finds extra, but if the lender finds extra, we say that the borrower gave extra for Ribis, and it is forbidden, except for Chachamim, who are permitted. Some say that even the Rambam's text means that the borrower found extra. Perhaps even the lender may keep extra (when it is not a mistake). We do not assume that it is post-loan Ribis (i.e. a token of appreciation without any prior stipulation). We do not assume that the borrower is a Rasha who will cause the lender to transgress, especially if this harms the borrower (he pays and also transgresses).

Mishneh l'Melech: The Magid Mishneh (Hilchos Ishus 1:4) said that people are not so careful about Isurim mid'Rabanan! He must hold that the Torah forbids post-loan Ribis.

Rambam (ibid): An amount that could be a mistake is one, two, five or 10. Perhaps Shimon counted five at a time or 10 at a time. Similarly, if he found one more than the number of fives or 10's, he must return it. Perhaps he was using coins to count the fives or 10's, and those coins became mixed with the 10's.

Lechem Mishneh: 'One or two' is when the local custom is to count one or two at a time. The Rambam says 'perhaps he was counting fives or 10's', for clearly people count this way. The Gemara mentions only fives or 10's', for in those days everyone counted this way.

Rosh (5:12): The amount that could be a mistake depends on how people normally count money in that region, e.g. two, three or four at a time. If the excess is this amount, without one or two extra, he must return the entire excess. If the excess is one or two more than this amount, the lender intentionally added it, and the borrower may keep it. This is if the lender did not claim it. If the lender says that he erred and gave too much, the borrower must return the excess.

Hagahos Maimoniyos (9, citing Tosfos 64a DH b'Isuraisa) and Hagahos Ashri: We count by ones, so for us any amount is a possible mistake.

Mordechai (433): Even though one must inform the owner when returning anything except for an Aveidah, also here the owner knows, for a person constantly checks his wallet. If one gave an excess that cannot be a mistaken and later asks for it back, Reuven need not return it. If one paid the price of cattle for a yoke, Tana'im argue about whether the money (price) proves that he intended for the cattle (Bava Basra 77b). If the money does not prove this, he cannot demand back the extra money.

Poskim

Shulchan Aruch (CM 232:2): If Reuven received money from Shimon, for a sale, loan or payment, and there were extra coins, even if Shimon did not claim it, Reuven must return it if it is an amount that could be a mistake. E.g., the excess is a whole number of 10's or fives without one or two left over, we can say that he erred between 50 and 40 or between 40 and 30. If the remainder is a multiple of five, people commonly count five at a time. If they were 55, he erred about the 10's like we said, and regarding the five extra he erred between three fives and four fives. If the excess was 15 or 25, he erred three or five times about the fives. If the excess exceeded a multiple of five by one, two, three or four, the entire excess is a gift, provided that the excess was not the number of fives or 10's.

Beis Yosef (DH u'Mah she'Chosav): Rashi explains like this. Also the Rambam says so.

Rebuttal (Lechem Mishneh): The Rambam is unlike Rashi. He holds like the Rif, that we attribute an error only to one five or 10. It is not normal to err like this more than once. If we would not say so, any amount can result if he counted ones and erred many times!

Note: This is unlike the Nimukei Yosef, who says that the Rif allows for multiple mistakes of five or 10. The Gemara mentioned that some count by 10's, even though any mistake of 10's could be attributed to twice as many mistakes when counting by fives. Perhaps this was to teach about when the coins used to keep track were mixed in. Tosfos says that indeed, for us any amount is a possible mistake, but the Rambam clearly disagrees.

SMA (5): If Reuven knows that Shimon did not count by fives and he found five extra, it is a gift. The same applies to all similar cases.

Shach (2): Darchei Moshe ha'Aruch (2) says that if the giver later says that he erred, R. Yerucham obligates returning the excess (like the Rosh), and the Mordechai (433) exempts. Shiltei ha'Giborim (Bava Kama 45b 1) exempts, and says that if a lender does not claim the loan, this shows that it was a gift and the borrower need not return it. This requires investigation.

Machaneh Efrayim (Ona'ah 22, cited in R. Akiva Eiger): Sefer ha'Terumos (46:4:3) says that if later Shimon says that he erred and gave too much, Reuven must return it. Even though we could say that Shimon intended for a gift and now wants to retract, Shimon claims Vadai and Reuven is unsure, so Reuven must pay.

Shulchan Aruch (ibid): If the excess was the number of fives or 10's, he must return it, lest the units he used to coiunt the fives or 10's got mixed in.

SMA (9): E.g. if he was owed 40 and received 44, we say that he counted 10 at a time and after each 10 put a Dinar on the side (to keep track), and later the four extra Dinarim became mixed with the 40. This is an error, and it must be returned. Likewise, if he received 48, he counted five at a time, and the eight extra Dinarim became mixed with the 40. The same applies to all similar cases.

Rema: In a place where people normally count money one or two at a time etc., this determines what is considered a possible mistake.