You should open a new thread for this topic if you'd like, please. I would be happy to discuss all the wars Egypt has had in great detail and particularly the October War of 1973. In the meantime, I'll just clarify a few things so that people reading this information for the first time get a clearer picture and not the wrong idea. Egypt has certainly suffered military defeats in most of these wars and I'll only say this as I don't wish to derail this awesome thread - suffice it to say that you can't paint all those wars with a broad brush stroke because of circumstances that existed at the time and the end results, the former reflected in 1956 and the latter in the 1973 October War or as it's more commonly portrayed by Israel and western literature as the Yom Kippur War. The crossing of the Suez Canal, the penetration through the supposed venerable Bar Lev Line and the holding of the Sinai territory by Egypt led to the withdrawal of Israel from half of it's gained territory of only 6 years after it occupied it in 1967. It also led to the reopening of the Suez Canal and the regaining of its revenues to Egypt. The cost on the battlefield for Israel was equivalent to the US losing 250,000 troops in Vietnam instead of 55,000. The impact was greater on Israel as the war's result forced it to lose it's grip on Sinai and it's resources. The whole gimmick of the 3rd Army being surrounded was ultimately a face saving feat for Israel to give it a stronger hand in negotiating at the cease fire, but it didn't help as the negotiations lingered well into January of the following year and by then, Sadat had amassed massive troops and was ready for anther offensive to destroy the narrow Israeli supply line to the south. Israel certainly didn't have the stomach for that and had no choice but to agree on a withdrawal. The 2nd Army to the north was strong and held its ground and constantly repelled the failed Israeli raids by Sharon prior to the cease fire. There is no doubt, that politically the victory was 100% in Egypt's favor as it brought in both superpowers to deal with Israel's expansionist endeavors and forced its eventual withdrawal across half of Sinai. A resounding political victory would've never been accomplished had there not been a semblance of a military one. If anything, most would concede it as a stalemate on the battlefield because of equal territorial exchanges and on-par superpower backing but you cannot disregard the end result which clearly favored Egypt.
So please consider these facts. A lot of these wars are not clear-cut battlefield victories or defeats but involve numerous factors. Had Israel won that war on the battlefield, do you think it would've given up an inch of Sinai? It would've held on to it like the Golan Heights and Jerusalem/West Bank. Not only did it give up the gained Egyptian and Israeli territory, it gave up the half of Sinai which technically, it still held after the war.
In 1956, Egypt was fighting Great Britain, France and Israel (not just Israel as you portrayed it) to rightfully take full control of the Suez Canal and nationalize it. It was a clear military defeat but who would've beaten that trio while being in the same position as Egypt was at the time? Israel also was forced to withdraw after that aggression and both GB and France were internationally humiliated and Nasser gained full control of the Suez Canal for Egypt. Not sure many other countries in a similar position as Egypt would've fared much better under those circumstances.