Content on Twitter's home timeline is selected and ordered by personalization algorithms. By consistently ranking certain content higher, these algorithms may amplify some messages while reducing the visibility of others. There's been intense public and scholarly debate about the possibility that some political groups benefit more from algorithmic amplification than others. We provide quantitative evidence from a long-running, massive-scale randomized experiment on the Twitter platform that committed a randomized control group including nearly 2M daily active accounts to a reverse-chronological content feed free of algorithmic personalization. We present two sets of findings. First, we studied Tweets by elected legislators from major political parties in 7 countries. Our results reveal a remarkably consistent trend: In 6 out of 7 countries studied, the mainstream political right enjoys higher algorithmic amplification than the mainstream political left. Consistent with this overall trend, our second set of findings studying the U.S. media landscape revealed that algorithmic amplification favours right-leaning news sources. We further looked at whether algorithms amplify far-left and far-right political groups more than moderate ones: contrary to prevailing public belief, we did not find evidence to support this hypothesis. We hope our findings will contribute to an evidence-based debate on the role personalization algorithms play in shaping political content consumption.