User blog comment:Kaido King of the Beasts/Big Mom Will Betray Kaido/@comment-24.13.236.50-20200529153846/@comment-108.83.222.210-20200529161009

Fighting her in Elbaf would be rather fitting. Besides, it would help the Strawhats gain the support of the giants because last time I checked they seem to hate Big Mom for multiple reasons. I find it highly unlikely that their mood towards her has improved in any way. Having said that, while it would be fitting Big Mom is an opportunist and has something of an ego likely due to her position as a Yonko.

As for how Luffy could beat Kaido, there are any number of possible outcomes that have been noted by people theorizing all over the place how this could occur. Some theories have betrayal, some have Kaido leaving and fighting them later, some have outside parties getting involved. I honestly cannot guess which one. Oda has created a situation where predicting what will happen next is rather difficult.