--- In vpFREE@yahoogroups.com, "Harry Porter" <harry.porter@v...>
wrote:
BJayGold wrote:
> How about a fantasy machine (which we're obviously talking
> about, considering the return) which pays 4164 coins for a five
coin
> Royal (52 card deck), and that is the only payoff. No other hand
> pays anything. The total return is 3.6%. Variance is 30.0 (feel
free
> to check it on WinPoker or FVP). Now add in 97.4% cash back.
Total
> is 101.0%. Do you honestly believe that this machine presents the
> same bankroll risk as a 101% return machine, variance of 30, zero
> cash back? I don't think so!!
Brian,
In an earlier reply to you I've 'fessed up to "dealing from less
than
a full deck" since the weekend. Truth is, I'm working on about 5
hours sleep now, having gotten up early to catch up on some work.
Unfortunately, this question is still nagging at me.
I've a follow up comment for your consideration, but I'm not going
to
stretch as far as drawing any conclusions. I'll leave that for
when I
truly feel my mind is clear as a bell. For now, just some food for
thought until my head is fully square on my shoulders 
------
It sits pretty firmly in my mind that two games with comparable
return
and variance present the same risk. Tom Ski's TSI index (referred
to
by Gene in his post, and a measure of how strongly a game optimizes
a
given bankroll) suggests that this is true since these are the only
variables that would impact TSI, assuming a constant wager per hour
in
each case.
Setting TSI aside, one can look at cashback as simply reducing the
wager on a bet, effected as a rebate. Consequently, adjusting
cashback doesn't change the variance of playing a game having a
given
paytable. You can confirm this by manually calculating variance and
increasing all of the pays (including what would otherwise be a
non-winning hand) by a constant amount.
So, I'm left with a bit of a quandry in your example. Both plays
present the same effective theo return to the player and both have
the
same variance.
Thus, from the perspective of what I believe I know to be fact, they
present the same bankroll risk. However, even in my original reply
to
Gene, I admitted that a "gut sense" would suggest that the low-
payout,
high-cashback machine with the same total return has lower risk.
Frankly, in my present state of mind, I'm not prepared to make a
call
until I'm in a better state to fully rationalize the "factual"
arugment. Nonetheless, if I had go with one or the other right now,
I'd stick by my original call of same bankroll risk.
Any comment on the "same variance/return" logic? I'm fully prepared
to accept that I've overlooked something here.
I think that as far as the TSI is concerned, Tomski assumed a
reasonable cash back percentage, almost always less than 1% in "real
life." If I am right about the reduced risk with greater cash back
amounts, it is only by a very small amount. Therefore, Tomski might
have just ignored this factor, since it would be completely swamped
by the variance/return factors.
As I said in my last post, I might be wrong. In any case, with real
world cash back, the risk reduction is either very small, or
nonexistent. Effects on bankroll required would be negligible in any
case. Also, in the real world, it would be extremely unlikely for a
player to have to choose between two plays such as Gene described,
with the only difference the minor risk reduction (if it exists) due
to the greater cash back percentage. Factors like strategy
proficiency, comps, distance, casino smokiness, and how cute the CWs
are, would all come in ahead of the very minor risk reduction factor,
at least for me!
Brian