A reverse Azuma's inequality for martingale

Question

I thought finding a reverse Azuma's inequality. Are there any inequality or lower bound looks like the following.

Suppose $\{X_k:k=0,1,2,3...\}$ is a martingale and $$P(|X_N-X_0|\ge t)\ge f(t)$$.

I saw a similar lower bound for binomial distribution, which is as the following.

Suppose $X$ follows Binomial(n,p),
$$P(X\ge k) \ge \frac{1}{\sqrt{2n}}\exp(-nD(\frac{k}{n}||p))$$.

Can I find a similar inequality in martingale?

Thanks !