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Kesuvos 93a discusses the case of a man who has three wives, and, for illustrative purposes, the wives’ Kesuvos are for $100, $200, and $300, respectively. The man dies. For the sake of simplicity, I will address the standard cases, as explained in the Gemara, rather than the more convoluted ones that are actually listed in the Mishnah. Further, my explanation of these cases reflects Rashi’s.

Case 1: The man’s estate is worth $100. Since everyone’s claim is at least $100, they all are claiming the entire estate, and as such, they split it equally, that is, $33.33 each.

Case 2: The man’s estate is worth $200. All three widows are claiming the first $100, and as such, they split that equally. However, only the two widows with the larger claims are claiming the second hundred - the one claiming $100 admits that she has no portion in the second $100. As such, only the widows claiming $200 and $300 take a share of this portion of the estate, splitting it $50-$50. Overall, the three widows split it $33.33-$83.33-$83.33.

Case 3: The man’s estate is worth $300. Following the same logic as the previous case, all three widows get $33.33 each from the first $100, two widows get $50 each from the second $100, and only one widow gets money from the last $100 and therefore gets the entire sum. They therefore split the entire estate $33.33-$83.33-$183.33.

And there the Gemara ends.

What happens when the estate is worth, say, $400? In that case, nobody is claiming the fourth $100. Does that mean they split it equally? Does the entire sum go to one widow, and the leftovers to a second widow? Does no widow get it, and it goes to the orphans as their inheritance? If this last option is correct, does that mean that when there’s $600, the estate goes to the widows and covers their claims entirely, or do they still fight over the first $300, and the other $300 are left for the orphans?

DonielF
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    You may well be aware if this, but Prof Aumann’s game theoretical analysis of the Mishnah in Ketubot is a gem. http://www.ma.huji.ac.il/~raumann/pdf/Game%20Theory%20in%20the%20Talmud%20BI.pdf – Joel K Aug 22 '18 at 03:57
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    Note that if you follow Prof Aumann's understanding of the mishnah (rather than the gemara's) you get a rule which applies to the cases you ask about. The results are tabulated in Table 6 (page 10 of the pdf). If there is $400, it's divided (50,125,225). If there is $600, it's divided (100,200,300) as one would expect. As his approach is (on its face) inconsistent with the gemara on which you based your question, I leave this as a comment rather than an answer. – Joel K Aug 22 '18 at 07:05
  • Note further that we don't actually pasken like this mishnah/gemara (which follows R. Natan) but instead like Rebbi. See Shulchan Aruch CM 104:10. According to this, when we have $400, it's split (100,150,150). – Joel K Aug 22 '18 at 07:19
  • @JoelK Thank you for bringing up Prof. Aumann’s article. I have indeed seen that before - it was actually my first introduction to this Gemara, which just underscored the problem you highlighted which is the main reason I don’t like it. That, and the fact that even the Gemara refused to get that convoluted. – DonielF Aug 22 '18 at 14:06
  • @JoelK As far as Rebbe vs. R’ Nassan - I know we don’t pasken like this, but Rebbe is just so boring. I mean, dividing things equally just takes the fun out of it. – DonielF Aug 22 '18 at 14:07

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Prof. Aumann has a Hebrew article here which contains a summary of the positions of the Rishonim who discuss your question. This is contained in section ג.6 which starts on page 6 of the linked pdf.

To summarize, where there is $400 available, the split is:

  1. Rif / Ra'avad - (55.56, 122.22, 222.22)

    The rule is that after we divide first 300 according to the principles in the gemara, we divide the additional amount according to the same rule. Here, all three women are claiming at least $66.67 of the additional $100, so we split that three ways and they each get $22.22. The remaining $33.33 is then split equally between the last two women (with claims $200 and $300) who are both claiming it.

  2. Ran - (66.67, 116.67, 216.67)

    The rule is that after we divide first 300 according to the principles in the gemara, we divide the additional amount equally between the three women. So here they each receive an additional $33.33.

  3. Ra'ah / Ritva - (33.33, 133.33, 233.33)

    The rule is that after we divide the first 300 according to the principles in the gemara, we then attempt to equate each of their losses. So in this case, each woman has lost $66.67.

Where the full $600 is available, then according to all Rishonim each woman receives the full value of her claim, so the split is (100, 200, 300).

Joel K
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  • So let me make sure I got this right. Let’s say that the estate is worth $500. According to the Rif, the first woman isn’t claiming anything more than the $466.67 mark, so she gets nothing of that. The second woman goes into the fifth hundred with $122.22, so she’s down $78.78 and therefore splits that evenly with the third woman, receiving $39.39, bringing her total to $161.61. The other $39.39 plus the remaining $22.22 goes to the third woman, bringing her total to $282.83. – DonielF Aug 22 '18 at 14:00
  • (Con’t) According to the Ran’s answer, they divide everything equally, so the fifth hundred is also divided $33.33 apiece. According to the Ritva, we divide up the overall $200 remaining to equate their losses. Therefore, they will all have $33.33 missing at the end, giving them $66.67, $166.67, and $266.67. Did I get all of that right? – DonielF Aug 22 '18 at 14:03
  • I agree with you re: Ran and Ritva. For Rif, I'm still not sure. I tried working it out and had to iterate three times, leading to a total split of (75, 162.5, 262.5) but I'm by no means sure that that's correct. – Joel K Aug 22 '18 at 14:23
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    By the way, thanks for this question! It's kept me pretty busy today... – Joel K Aug 22 '18 at 14:23
  • To clarify re: Rif in the $500 case. I don’t understand what you mean by “the first woman isn’t claiming anything more than the $466.67 mark”. The way I look at it, after the first 300 are divided, the remaining claims are (66.67, 116.67, 116.67). We still have 200 to divide. So divide 116.67 of that according to the gemara’s rules. You then have total awards of (55.56, 130.56, 230.56). Now you have 83.33 to divide and remaining claims of (44.44, 69.44, 69.44). So divide 69.44 of the 83.33 according to the rules. Wash, rinse and repeat and you eventually get total awards of (75, 162.5, 262.5). – Joel K Aug 22 '18 at 15:13