Strategy difference between Ultimate TX Hold 'Em and Heads Up Hold 'Em

I understand these two games to be essentially identical, the big difference being that a 4x raise is allowed pre-flop in UTHE, only 3x in HUHE. Yet the Wizard's recommended strategy is quite different for each game (links below). Specifically, in UTHE the strategy is to raise 4xs with offsuit K5, Q8, or J10 or better. In HUHE, the strategy is to check these hands, and raise 3xs only with offsuit K7, Q10 or better. This is counter-intuitive. Why would the difference between a 4x and 3x raise alter the strategy in this way?

https://wizardofodds.com/games/ultimate-texas-hold-em/
https://wizardofodds.com/games/heads-up-hold-em/

Quote: Jumboshrimps

I understand these two games to be essentially identical, the big difference being that a 4x raise is allowed pre-flop in UTHE, only 3x in HUHE. Yet the Wizard's recommended strategy is quite different for each game (links below). Specifically, in UTHE the strategy is to raise 4xs with offsuit K5, Q8, or J10 or better. In HUHE, the strategy is to check these hands, and raise 3xs only with offsuit K7, Q10 or better. This is counter-intuitive. Why would the difference between a 4x and 3x raise alter the strategy in this way?

https://wizardofodds.com/games/ultimate-texas-hold-em/
https://wizardofodds.com/games/heads-up-hold-em/

Stab in the dark, I'm guessing because the UTH is a 4x raise instead of a 3x raise, the relative value of being able to fold later in the hand is less. That would make sense, since the threshold hands for raising on HUHE are better hands.

EDIT: For example, your Q8 off suit hand. The UTH calculator says:

Average Raise Value: -0.069429
Average Check Value: -0.092563

So, it's a negative proposition either way, but if you're going to win that particular hand, the best mathematical play is to win as much as possible.

With Q-8 offsuit in HUHE, we get an average value of -0.037723, according to the chart:

https://wizardofodds.com/games/heads-up-hold-em/1/

The difference in value between the checks would be due to the, "Bad Beat," odds offered on the second game. No such thing exists on UTH. Thus, when you combine the relative change in value of the ability to fold with the bad beat payouts, a few of the starting max raise hands become different.