Challengee vs Challenger

challenger named Ger proposed the following wager to a challengee named Gee:

"Select some number of cards from this standard deck; shuffle them, and place the cards in a stack face down.  Turn the cards face up one at a time until I say stop.  I will wager that I can identify the highest card in the stack."

"You're joking," scoffed Gee.  "You will simply wait until I turn up the last card from the stack, point at the highest, and take my money."

Ger chuckled.  "Not at all.  I will pick the highest card as it is revealed to me."

"How will I determine if your choice is right?"

"Easy," Ger replied.  "You will have looked at all the cards in the stack before shuffling them."

"Do we assume aces are low, kings are high?" asked Gee

"As you wish."

"And the suits, will they be in the conventional order: Clubs, Diamonds, Hearts, Spades?"

"Fine by me."

"Inasmuch as you know the highest card, I will simply read your mind."

Gee looked askance at Ger.  "How many cards am I allowed to select?"

"As many as you want."

"What if the card you pick is not the highest?"

"You win the bet."

"What if you pass up the highest card?"

"You win the bet."

"In your dreams," Ger grunted.  "But I will let you offer me low odds."

"How low?

"I'll accept two-to-one."

It was Gee's turn to chuckle.  "Surely not two-to-one for any number of cards!"

Ger nodded.  "No matter what the size of the stack."

 ...to the challengee, Gee? ...to the challenger, Ger?