All-In every hand, how big of a stack do you need...

[fatdave]

Heads up no-limit hold 'em: You and your opponent are going to go all in every hand, no matter what. How many times larger than your opponents stack must your stack be to make their odds of winning it all 1%?

Originally I thought it may be 99-1, but if they double up on the first hand, that will change... then it will especially change if they double up again on the second hand.

If you change it so that they will only go all in with Ax, Kx, any broadway, any pair, any suited connector or any connector 56o and above, while you still call with any two cards, how big must your stack be to make their odds still 1%?