Harry wrote, "regarding the average Wheel payoff of 428: A bonus
equal to the quad cycle (with optimum return) would, of course, be EV
neutral."
Bob Dancer wrote:
That is tautologically true but it hides some basic truths.
8/5 Bonus Wheel Poker returns 99.59% --- which is considerably higher
than "EV neutral" --- even though the 428 figure closely mirrors the
quad frequency of Bonus Poker. The explanation for this riddle is
that the strategy is considerably different for Wheel Poker.
The net effect is that the quad cycle is shorter in properly played
Wheel Poker than in the base game.
To call it "tautologically true" is to be somewhat cruelly kind, no,
Bob? 
(or should that be "kindly cruel").
You're right, of course -- it couldn't possibly be "EV neutral".
There's a modestly perverse nature to the economics of the game. In
analyzing the game you could (if you wished), break the wager/payoff
into two components: 5 coins wagered against the standard paytable; 1
coin wagered against the possibility of hitting a bonus.
The 1 coin wager is going to argue in favor of playing harder for
quads. However, the harder you play for a quad, the more you weaken
your ER on the 5 coin wager portion (by playing a sub-optimal strategy
for that portion of the wager).
In order for the 1-coin wager to compensate for that weakening of the
5-coin ER, it's necessary that that the 1-coin portion of the wager
have a positive ER. That means that the average bonus payout must
exceed the bonus cycle of the optimized Wheel strategy (in other
words, if the quad cycle under optimal strategy were 400 hands, the
bonus must be something in excess of 400 cr).
In the 8/5 BP game you note, optimal ER Wheel strategy reduces the
quad cycle from 423 to 406. A bonus payout of 428 yields an ER of
105.4% on the bonus bet. When that premium return is allocated
against the base 5 coin wager, it's a 1.1% kicker to game ER.
However, as noted, playing for quads weakens the 5-coin wager -- by
.7, yielding a net game improvement from the Wheel bonus feature of .4%.
btw, is the stated 428 bonus a constant across all non-wild card
games? (As remarked separately, I presume it's something different in
the deuces games.)
- Harry