Cogno Scienti wrote:
I wanted to wait until we agreed on the 0.5%, since your thesis was
that the 0.25% additional ER made up for the top jackpot. I guess
it only makes up for half of it.We agreed that "variance" isn't sufficient to identify risk until
many cycles of the top jackpot. With 1.5% of the return having a
cycle 2x, 4x, and 8x single line, the additional ER is not
sufficient to compensate an unlucky run even in a million hands.In the medium term, it's not only the top jackpot. Quads on the top
three lines count for almost 4.5% of the return and dry spells will
last 2x, 4x, and 8x longer.So what are we trying to establish? I think people are interested
in three things: the ER, which we all agree on; the short-term
bankroll requirements (how much do I need to bring to the casino to
play n hands); and the long-term risk (how likely is it I'll go
broke or die before hitting my ER).For short-term bankroll requirements it would probably be easiest
to run simulations. The added length of each cycle is ameliorated
somewhat by the regression to the mean in the shorter cycles that
occur simultaneously. I'm guessing it's about the same as a
single-line game of the same total wager, which I think was your
point in the first place.For long-term risk, the longest cycle is 8x the single-line game,
so I'm asserting that by some measure the game is 8x worse than
single line in that respect. The added ER does make up for part of
it, so maybe it's only 4x worse than single line. But denomination
is irrelevant to this calculation, so at least with respect to
long-term risk MS is significantly riskier than a single-line game
of the same total wager.Cogno
I don't want you to think I don't have a healthy respect for the long-tailed risk associated with high-paying hands played infrequently on the upper Levels. However, I believe you under appreciate just how much other game aspects counter that risk.
I noted the higher return, and my point is that it's not essential that that return entirely counterbalance the 4th Level royal to meaningfully reduce the player downside risk.
One means by which to re-express variance in a manner that puts MS and single line play on a more equal footing would be to reduce the top line RF payout to a value that gives play an ER equal to single line play. (Anything paid over and above that represents adequate return for added variance ... just in the same way that you wouldn't cite added variance derived from the climb of a progressive as undesirable risk.)
Using my calculator (which I sent you a copy of), cutting the 4th Level RF in half results in a game EV of 99.539%. The adjusted variance is 14.9.
That's a substantial reduction in variance from single line play and strongly suggests that, as I indicated before, the higher overall hit frequency and reduced pay per hit as a consequence of playing 2 hands per play on average serve to greatly reduce play variance.
With that 99.539% of return, as you note, Level 4 quads are quite a force to be reckoned with, contributing 1.5% of game return and having a long cycle of 3400 plays. But, by the time one plays through 70K plays, things start moving into "long-term" territory.
The Level 3 RF, with 0.5% return, has a 160,000 play cycle. The Level 2, with similar return, 80,000 plays. No doubt that means that it will take a lot of play before you have strong confidence of being within 1% of ER. But I see a lot of reasons why play would approach +/-2% of ER as quickly, if not more quickly than single line play.
Bottom line, over short term and longer term play I anticipate that a player who has the bankroll to comfortably play single line play should find that MS play, at the same total wager per play, is also comfortable.
I don't know if VP for Winners includes the bankroll component for it's MS game. (My copy has been corrupted and I haven't sought a fix.) If it does, I would anticipate that session and overall numbers would back up my gut feeling here. I'm prepared to be mistaken.