She pursued equal pay relentlessly. A pragmatist, she arrived at a meeting with the US Open’s tournament director in 1972 with corporate funds in hand to bridge the prize gap. She vowed that most of the top women would not participate the following year if he refused. (He agreed.) She organised the Women’s Tennis Association in 1973 and became its first president. Later that summer she won Wimbledon in singles, doubles and mixed doubles. Today women compete for equal prize money in all four Grand Slam competitions. The world’s best-paid female athlete is routinely a tennis player.

Ms King’s highest-profile match was the “Battle of the Sexes” in 1973. Bobby Riggs, a loudmouth with hidebound views and a knack for publicity, challenged her to a friendly exhibition. She recognised the stakes and took care not to underestimate her opponent, studying his game and developing a plan to make the older man run. And run him she did, under the carnival lights of the Houston Astrodome, with 30,000 people cheering and 90m more tuning in at home. Countless admirers later told her what her win meant to them, she writes, including Barack Obama, who saw her practise in Hawaii in the 1970s.

True to its title, “All In” is bracingly candid. Alongside the sporting and political battles it tells of the eating disorder from which Ms King suffered, a sexual assault she experienced as a teenager and the whirlwind of being outed as a lesbian by a former lover in 1981. Ms King does nothing by half-measures — so much the better for readers, sport and the many women she encouraged and empowered.

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