This is a bit of something that delves into the strategic character of warfare rather then something that classifies as traditional historical sources of underlying causes and rationale but let me lay context with what made Percival's numerical advantage nearly pointless.

By 1942 the Garrison of Singapore was rather significant with a standing strength of 85,000 soldiers, the equivalent, on paper at least, of just over four divisions. There were at least 70,000 front-line troops in 38 infantry battalions—13 British, six Australian, 17 Indian, two Malayan—and three machine-gun battalions and if at the par standard of the German, American or even Japanese divisions that the British worked with and fought against it would be extremely difficult to dislodge. However the force in reality was what is more equivalent to a hodgepodge of different forces and quality of soldiers.

For example, the recently arrived British 18th Infantry Division was at full strength and fought as such. But at the same time it's forces were composed entirely of newly recruited men with little experience and somewhat poor training. More experienced or localized units like the Malayans and other British units had fought the Japanese for 3 months prior and had been significantly damaged or demoralized by the defeats inflicted upon them in the months prior. This left a large but inconsistent force which was also extremely top heavy. (15,000 of the armed forces personal in Singapore were largely administrative officers or enlisted men!)

Another thing both the British and Japanese knew was the idea of a "Fortress Singapore" was not as pronounced as the British often boasted. In 1940 a German merchant raider called the Atlantis was able to capture a British steamer ship in the Indian ocean carrying papers bound for the desk of Air Marshall Sir Robert Brooke-Popham who was commander of Anglo contingent in the far east. These papers precisely and thoroughly outlined the weakness of Singapore's strong defenses (Including how her strong artillery could only be pointed seaward which encouraged Japanese invasion via the Malay peninsula) and to great effect were passed over from the Germans to the Japanese armed forces by December 1940. Well before the British even expected a conflict in Singapore the Japanese knew exactly how and where to take the fortress the British relied upon so significantly in Malaya.

This intelligence was compounded again when Japan managed to break British military communication codes and again found a trove of information saying Singapore was vulnerable. The Japanese had broken the British Army's codes and in January 1941, the Second Department (the intelligence-gathering arm) of the Imperial Army had interpreted and read a message from Singapore to London complaining in much detail about the weak state of "Fortress Singapore", a message that was so frank in its admission of weakness that the Japanese at first suspected it was a British plant.

Although many point towards the fact the Japanese plans for invading Singapore were reached in June 1940, these frank and stark admitting of the British about the vulnerabilities were something both General Percival and Yamashita knew quite well. And it gave Yamashita much more abandon to assault the large British garrison which was both irregular in composition and poor in it's self confidence to fight.

Percival not only had to compete with such downfalls, but also the fact coordination among Commonwealth forces was abysmal and his own strategic plans for defending Singapore were not in line with where the Japanese actually would strike. Percival incorrectly guessed that the Japanese would land forces on the north-east side of Singapore, ignoring advice that the north-west was a more likely direction of attack (where the Straits of Johor were the narrowest and a series of river mouths provided cover for the launching of water craft). This was encouraged by the deliberate movement of enemy troops in this sector to deceive the British. As such a large portion of defense equipment and resources had been incorrectly allocated to the north east sector, where the most complete and freshest formation—the British 18th Division—was deployed, while the incomplete Australian 8th Division sector with just two brigades had no serious fixed defensive works or obstacles. To compound matters, Percival had ordered the Australians to defend forward so as to cover the waterway, yet this meant they were immediately fully committed to any fighting, limiting their flexibility, whilst also reducing their defensive depth.

One cannot say Percival was a poor commander as much as Yashimata was an exceptional one. The Tiger of Malaya as was he was later called was very unique in his attention to detail and thorough capacity to deceive in battle. Making use of dedicated if often outnumbered forces he was able to make difficult battles colossal successes for the Japanese Empire. His own forces were extremely experienced, high morale and high dedication forces composed of men such as the Japanese Imperial Guard, seasoned veterans of the Chinese and Indochinese campaign like the 5th and 18th divisions that also held coordinated armored components which the British both lacked and could not counter in turn.

Percival's decision was ridiculed much more extensively at the time then he is now as the circumstances are more understandable, he had a force that was made up of a massive range of quality and characters that was difficult to wield and properly use. And he also had to compete with an efficient, talented and extremely dedicated Japanese commander who had at the time some of the most seasoned and loyal forces his empire could muster.

The British and Japanese both knew exactly what they could do with the circumstances around them. The difference was the Japanese also could measure their opponents at the same time as themselves. I believe to finish a quote from the mastermind of the fall of Singapore can give you your answer.

"My attack on Singapore was a bluff – a bluff that worked. I had 30,000 men and was outnumbered more than three to one. I knew that if I had to fight for long for Singapore, I would be beaten. That is why the surrender had to be at once. I was very frightened all the time that the British would discover our numerical weakness and lack of supplies and force me into disastrous street fighting." - Tomoyuki Yamashita

Greetings, I'm a bit late to the party but I'd like to add a few things/expand upon a few points since this is my area of expertise.

As the maxim goes, its not about the size, but about how you use it. The British here had a numerical superiority in terms of sheer troop numbers but suffered from serious strategic issues. First and foremost was the lack of naval superiority. The fundamentals of the Singapore Strategy which was the British would dispatch a fleet to relieve the garrison of Malaya before driving north to Hong Kong. While this being flawed from the start since the arrival of the fleet would not necessarily transform the situation, this was always subject to availability of the RN and subordinate to needs of other theaters. Prior to the start of the Malayan Campaign the RN was heavily engaged in the Mediterranean and Atlantic which resulted in their failure to dispatch an adequate battlegroup to Singapore. Following the destruction of Force Z after Admiral Phillps failed sortie to disrupt the landings, the Japanese achieved total naval control. This lack of the British ability to interdict and future landings forced Percival to keep troops (8th Australian Division and the Singapore Fortress) in reserve to combat any potential landings that would outflank him mitigating his numerical superiority.

Next we need to look at the force composition on both sides. The British forces were comprised of Heath's III Indian Corps made primary of Sepoys who had their experienced troops gradually siphoned from them to serve in North Africa. Pericival had a few British Battalions such as the East Surreys and the Argyll and Sutherland Highlanders but these were attached to other larger formations. Next there was the 8th Australian Division under Bennett and lastly the various Fortress formations which were garrison troops. The commonwealth forces were fundamentally a coalition group which faced numerous coordination and logistic problems. For instance for the Indian troops it was a logistical nightmare to supply them due to the diverse dietary needs due to religion which further complicated things once Muslim and Hindu Indian troops were amalgamated into combined units later in the campaign. Generals such as Bennett and Heath also did not coordinate adequately with Percival with Heath constantly on the retreat and Bennett constantly demanding Australians be sent into action in order to win glory. On the other hand the Japanese had a much more homogeneous force which all had the same supply requirements made of veteran troops which Yamashita had effective control off. This disparity in level of coordination and homogeneity of forces allowed for Yamashita to employ his troops more effectively then Percival.

Lastly we should look at the actual campaign itself. Singapore itself was by no means a fortress from the landward side as the British had identified it as a decisive point to the defense of the Peninsular too late to make adequate preparations. In addition, the RAF had unilaterally set up forward airbases without consulting the other services placing them in positions near the coast to increase their aircraft's operating ranges but sacrificing defensibly. Percival was thus required to defend these airbases which further divided his forces into penny packets while the Japanese achieved a high level of force concentration. The failure to launch Operation Matador which was an attempt to preemptively strike at the Japanese landings and cut off the line of advance also threw the British further off tempo as the troops only managed at hasty defense at Jitra when their orders were changed. As said prior, Percival also kept substantial reserves in case of naval landings leaving Heaths III Corps to bear the brunt of the fighting in the North. Yamashita used all 3 of his Divisions immediately in the campaign against Heaths 2 which led to the mauling of III Corps and the British fighting at a numerical disadvantage. By the time the Australians relieved the Indian forces, III Corps was so badly battered that they failed to be a cohesive fighting unit. There was also numerous other things that undermined the British defense such as lack of coordination with the civil colonial administration and Percival's rejection of suggestions to construct defensive fallback positions in Johore due to him believing they were bad for morale.

By the time the battle of Singapore had started, the British had been reinforced by the 18th Division but their fighting strength had suffered so badly that saying they still had a numerical advantage would not be very nuanced. While they did have a higher total strength, one must also remember that this number also included support troops which were not suited to frontline combat thus not reflecting their true combat potential. The decisive moment came when the Japanese secured the British supply reserves and the reservoir at the Battle of Bukit Timah hill. This gave Percival two options, either to surrender or launch a last ditch counter attack to reclaim the cache and continue to resist or die trying. Unknown to him, Yamashita's attack was also loosing cohesion and was running out of supplies with his artillery ammunition close to exhaustion. In hindsight, the potential outcome of the counterattack is unclear and in my personal opinion is only a viable option given knowledge of Yamashita's condition which Percival would not be prevailed to. Thus Percival elected to surrender instead of increasing the number of casualties.

Military historians are relatively critical of Percival citing that his leadership lacked aggressive spirit due to him holding excessive reserves throughout the campaign. He even had to be overruled by Wavell after he took over Far East Command late into the Malayan Campaign to commit reserves in Singapore to the front despite Percival's continued fears of a direct landing in Singapore. He has also been criticized for his lack leadership in the sense that he failed to adequately inspire or manage his subordinates like Heath and Bennett who did not want to cooperate with his battleplans and did not have the will to remove them and place someone else more supportive of his command in their place. However, in hindsight most Historians that specialize in this campaign such Brian Farrell , Ong Chit Chung and Malcolm Muffert agree that Percival was the victim of the strategic failures of prior British decisions and the general convoluted nature of the Singapore Strategy. This decision is remembered as a great defeat for the British and thus is unpopular but none of the Historians seem overly critical as they understand the circumstance that Percival was dealt with. While Percival was blamed for making poor decisions and being overly cautions, none of the sources I have read placing him as the primary reason for the defeat and thus do not disagree with the surrender decision from a strategic point of view.

Sources

Books:

The Defence and fall of Singapore 1940-1942 - Brian P. Farrell

Singapore Burning: Heroism and Surrender in WWII - Colin Smith

Operation Matador: World War II - Ong Chit Chung

Papers:

The Worst Disaster: The Decisive Point and the Fall of Singapore - Cmdr. Don C. Murray

Malayan Campaign 1941 - 1942 from Goh Keng Swee Command & Staff College, Singapore Armed Forces - Brain Farrell, Lim Choo Hoon, Gurbachan Singh, Wong Chee Wai

Thanks for the detailed response! I was not aware of the intelligence breakthroughs that were very advantageous to the Japanese.

I'm not sure what to make of the quote that you ended with. Bluffing usually indicates that if both hands were played correctly and nobody is fooled into surrendering/folding, the person who is bluffing has the weaker hand and should lose. Yamashita's quote seems to indicate that if the British did not surrender the Japanese would eventually be defeated. This would seem to go against the idea that the British situation, due to positioning and manpower, was not winnable. If Yamashita did actually have the advantage (due to lack of trained British fighters, too many administrative officers, difficult position to defend) then there would be no need to bluff. Yamashita's own words ("I was frightened all the time that the British would discover our numerical weakness and lack of supplies and force me into disastrous street fighting.") seem to indicate that he was very vulnerable to defeat if the British continued the fight.