The 1-5 May 1942 war games are very well-attested to in the historiography on Midway. While some of the details of the war games are hearsay given that a good many of the principle actors (eg Yamamoto, Ugaki, Nagumo, etc.) did not survive the war, the IJN did convene a series of war games on board the superbattleship Yamato. The main exercise area was the battleship's mess and various cabins simulated portions of the fleets with runners acting as substitutes for radio communications. The games had umpires, Ugaki Matome was one of them, and damage was simulated by dice. One war game did feature a red forces (the USN) sailing at the blue forces (the IJN) while the Midway invasion was underway. This flank attack did sink three IJN carriers. Another simulation featured a lucky roll of the dice by the blue team's land-based airpower sinking two carriers. In both cases Ugaki directly overruled the results of these attacks claiming that such a scenario was unlikely.

Before attacking the IJN for short-sightedness and Victory Disease, it should be noted that these two games were not quite what unfolded at Midway. In the first case, the red forces showed up in the waters around Midway sooner than expected, but the assumption was still that the USN would be reacting to Japanese moves to Midway and not already aware of Japanese objectives. The American carriers intervened against Nagumo's carriers before the Midway invasion force even got close to the island. And Midway's land-based airpower was fairly ineffective during the battle even though it caused considerable consternation within Kido Butai. So the umpires' concerns that these unfavorable results were unlikely were not completely groundless.

That said, the war games were in the words of Shattered Sword authors a "rubber stamp" for Yamamoto's Midway plans:

The games had served as a monologue. There had been no intellectual discourse, no learning; the entire affair had been a mockery of professional staff work. The net result was that Nagumo would go to battle armed with practically nothing in the way of realistic contingency plans. Whatever difficulties arose would be his to handle, alone.

These war games were not about testing the validity of the planned invasion and sea battle. While it is difficult to speculate on the motives of for holding these games, again many of the participants did not survive the war, it was possible that Yamamoto convened them to beat down skepticism of the Midway operation. Nagumo reportedly was not enthusiastic about the plan. But it is also possible that the war games were just simply the IJN going through the motions of planning a major operation. War gaming was something modern militaries undertake and have done so regularly since the Napoleonic period. In this case though, the Midway war games were egregiously sloppy and did little to resolve the many problems of the Japanese plan to invade Midway and bring the USN carriers to heel.

Just want to add, that in Shattered Sword, the authors describe the attitude of those present at the war games, when asked by Yamamoto what they would do if the U.S. showed up unexpectedly, their attitude was more like "We'll deal with it". This is also discussed in Midway, the Battle that Doomed Japan: The Japanese Navy's Story by Masatake Okumiya and Mitsuo Fuchida (some of the quotes regarding the war games in Shattered Sword are taken from Fuchida and Okumiya's book).

This attitude seems laughable considering how much the Japanese were caught off guard at Midway, but part of the reason this attitude MIGHT seem more defensible is in the context of the reconnaissance the Japanese expected to give them advanced warning of attacking carriers. There were at least three ways in which the Japanese expected to be alerted to U.S. carrier presence in the area. One of these was unsuccessful in part due to U.S. code breaking. The other two failed miserably:

1. Operation K - this was an operation (in the context of the upcoming Operation MI) to reconnoiter Pearl Harbor and determined if the carriers were present there. This required flying boats that needed to be refuelled via submarines to reach Hawaii. Their intended refuelling point was guarded by American warships and not approachable by the subs anymore, so this was unsuccessful.

2. The Japanese assembled a picket of submarines to monitor the waters to the east of Midway, however this picket was late in being completely assembled, and the U.S. carriers had already sortied past the picket. In addition, the late assembly of the picket was not even communicated to IJN high command, so Nagumo didn't even know that this picket was unreliable.

3. The other reconnaissance is to launch recon planes directly from the carrier task force (either from the carrier or escorting destroyers) in a spoke pattern towards the area to be searched. This is distinct from the regular CAP. At Midway, 7 recon planes were used, but as discussed in Shattered Sword, the area they had to search was about the size of Sweden, and 7 planes is simply not adequate and has almost no margin of error. Utilizing a much larger number of planes with some overlap in adjacent plane's search area would have been a safer approach according to the authors of Shattered Sword. One failure that occurred, was that one of the planes involved in the search should have detected one of the U.S. carrier task forces very early in the morning but did not, by the time it was detected by another plane a few hours later, it was too late for Nagumo to do much about the bombers already heading towards Kido Butai.

Source: Shattered Sword