It’s debatable whether this quip is true, but is such a distinction even wise? Clearly Fiorina was appealing to voters fed up with the rhetoric-to-action ratio in politics, but it’s unclear if appealing to gender strengthens her case.

For those in business leadership, does playing the woman card hurt more than it helps?

Playing up gender might be an honest attempt to find an advantage in a game where you’re an underdog (or wanting to score a laugh), but it can bring trouble. Leaders who play the gender card shouldn’t be surprised or call foul when, like a game of rummy, that same card gets picked up by other players and is used against them. For example, if women are billed as “good executors,” they are naturally steered toward roles in project management or administration—positions where they make a valuable contribution but where careers often plateau. Meanwhile, chiding men as “all talk” positions them for roles as spokespeople, sponsors, advisors, dealmakers, and keynoters—all critical roles for advancement to senior management. A study conducted by Catalyst, Inc. and the University of Michigan found that men look at female leaders with more negative stereotypes than women do. When women talk up the advantages their gender brings, it invites men to conjure up their own generalizations.

However, the real danger with playing the gender card is a collective threat that traps our organizations in antiquated, ineffective leadership models at a time when we need agility. The facts are out there. Female leadership is crucial for organizations to perform and compete at the highest level. Yet a Women in the Workplace study concluded that women face greater barriers to advancement and a steeper path to leadership, and report—more so than men—feeling pressure along the way. When we operate from pre-fabricated views of gender strength, we further increase this pressure and limit the range of motion and contribution of both men and women.

A C-level executive I worked with closely once commented that he liked working with me because, as he put it, “you are just you.” He said, “You don’t try to be one of the guys, but you also don’t overplay the feminine charm.” I was lucky to work in an environment that allowed me to be myself. Unfortunately, many women of my generation have contorted themselves to fit into a male-dominated world, choosing between ill-fitting models of leadership. Some adopted the “man-up” model. Dressed in power suits, they acted tougher than nails, showed no fear, and attempted to out-men the men. Others fell into the “mama bear” archetype in which they nurtured, protected, and rescued people and projects in danger. In my own research, I’ve found that leaders who operate from these leadership caricatures can have massively diminishing effects. For example, “manning up” can hold back team members and stop them from taking risks, while filling the “mama bear” role tends to prevent staff from taking accountability and learning from hardship.

Leaders are most credible and command the best in others when they are authentic—being themselves rather than acting out a role. As professors Rob Goffee and Gareth Jones said, “Simply put, people will not follow a leader they feel is unauthentic.” While there may be some actual differences in how men and women lead, there seems to be far more variation within a given gender than between the genders. We need to open up the full range of styles and strengths to women and men. If women are to be freed from limiting stereotypes, then men must be liberated from them, too. For women to be big, men can’t be made to be small.

Leaders should think twice before playing the gender card. Rather than allude to the vague virtues of their genders, the most powerful leaders focus on playing their chips right. When leaders dispense their ideas in small but intense doses, their voices are stronger and people around them have room to step up. And, when we stop indulging gender stereotypes, all leaders can operate with full authenticity, which invites full contribution. When the pressure’s on, smart organizations must ensure all available players are in the game.

Liz Wiseman is president of Wiseman Group. She is the author of three best-selling books: Rookie Smarts: Why Learning Beats Knowing in the New Game of Work, Multipliers: How the Best Leaders Make Everyone Smarter and The Multiplier Effect: Tapping the Genius Inside Our Schools. She has conducted significant research in the field of leadership and collective intelligence.