The 32-year-old who is now Britain's leading female entrant following the withdrawal through injury of last year's champion, Paula Radcliffe, appeared temporarily lost for words. "To be honest I haven't given that a moment's thought," she eventually responded. "I'd probably have a few drinks at a post-race party."
The bookies share her doubts - Yamauchi's victory odds are 33-1 - but her veteran coach, Bob Parker, has faith about the wisdom of putting money on her. "I am, mate," said the 76-year-old who guided the spectacular track career of the London race director, Dave Bedford, more than 30 years ago. "The others can trip up, can't they?"
Parker still recalls being unable to get a bet on his man before the 10,000 metres at the 1973 AAA Championships, where the odds against the world record being beaten were 50-1. Bedford took more than eight seconds off the mark. No wonder the coach still winces at the memory.
The experience of coaching Bedford and the Oxford-educated Yamauchi has been, as Parker readily acknowledges, "slightly different". He added, with a grin: "Dave was more the maniac type." Years after his colourful career had come to an end, Bedford decided on the night before the race to run the London Marathon after taking a bet at the nightclub he ran in Luton.
Yamauchi's approach to marathon running is more measured. And although she is not expected to emulate Radcliffe's achievements tomorrow, she will hope to maintain the striking progress she has made since returning to the sport in 2003 after spending five years working at the British Embassy in Tokyo.
Having finished 17th on her marathon debut in the 2004 London race she improved to 10th place last year and then placed 18th in the World Championships before setting a personal best of 2hr 27min 38sec in November's Tokyo marathon.
In Melbourne last month she achieved her highest-profile success so far by outpacing the home runner Benita Johnson in the closing stages of the Commonwealth 10,000 metres final to earn a bronze medal. It was another personal best - by more than 45 seconds.
Yamauchi's overriding ambition is to compete in the 2008 Olympics, and to that end she has taken two years' unpaid leave in order to train full-time. Her runs take place along the banks of the River Tamagawa, a short distance from the flat in a Tokyo suburb which she shares with her husband, Shige, whom she met while working at the Embassy.
Yamauchi might have made a sporting reputation for herself far earlier, involving her maiden name of Myers, having won the 1998 National Cross-Country title and established herself as an international performer. But her career took priority.
After reading Politics, Philosophy and Economics at St Anne's College, Oxford, she completed a Masters degree at the London School of Economics and then joined the Foreign Office in 1996, taking up a posting in Tokyo two years later. Naturally, she learned Japanese beforehand.
"It was tough," she admitted. "One of the three alphabets, Kanji, is derived from Chinese symbols. There are many thousands of those, and you need to learn at least 2,000 to be able to read a newspaper. But there are several different readings for each of the characters..."
The effectiveness of her efforts was put to the most fearsome of tests in 2000, when she had to act as an interpreter for Baroness Thatcher when she visited the Embassy.
"The man sitting next to Mrs Thatcher didn't speak English, so I helped the conversation," Yamauchi recalled. "It was just a discussion about what was happening in England and Japan. But she was a very statesmanlike presence."
Other tasks included helping Tony Blair's bodyguards liaise with their hosts over security arrangements during a G8 summit, and helping with a public relations drive before the 2002 World Cup to convince the Japanese public that not all England football fans were necessarily hooligans.
The Japanese lifestyle seems to suit Yamauchi, whose flat has a distant view of Mount Fuji. And it is a happy coincidence that marathon running is something the Japanese revere.
"The marathon requires patience, hard work, application and determination," Yamauchi said. "These are all qualities the Japanese particularly appreciate. I have a similar approach to life." While she experiences none of the alienation evident in the film Lost In Translation - "I think it is a trivialised view of Japan" - she is occasionally self-conscious in her adopted culture.
"The population is so homogenous that foreigners do stand out," she said. "But the Japanese people are very friendly. I do miss British culture, but we take the Financial Times every day, and I listen to the Radio 4 Today programme every afternoon on my personal computer." Yamauchi also appreciates the local cuisine, and is taking a course in Japanese cookery.
"Japanese food is very good for marathon runners because it's low on fat and high in carbohydrates," she said. "I don't particularly like sushi but I love things like hijiki, which is a type of seaweed, and soba noodles." She mentions only one specific problem with her Japanese lifestyle - no fig rolls. Somehow, you sense she will get over it.