Hah!
Just get somebody to bet against "Nelson" with modest odds, but don't let him/her know that two Nelsons are potential Jeffords.....
Then bet the opposite way: Either one of your two Nelson's does change (and you win), or the wrong "Nelson" (who he bet for) doesn't change (and you win), even if one does change, or wrong "Nelson" doesn't change, and you win, even if one doesn't change.
You are a genious!