Money Management & Bet Optimization
On my latest
podcast, Dave Schwartz and I had a spirited debate about betting strategies
and/or money management (depending on one’s perspective).
Dave made the argument that, while a betting strategy can alter one’s ROI, it cannot turn a
positive expectancy into a negative one — or vice-versa. To prove the former, he
used the example of a 30 percent win bettor who averages an $8 mutuel.
“Let’s say you are a positive expectancy player — that is,
you have the best of it,” The
Horse Handicapping Authority said on my July
23 show. “And your records indicate that you get a 30 percent hit rate and
your average mutuel is $8. … $2.40 is your average return ($8 x 0.3 = $2.40)
for a $2 bet.
“So, suppose you parlay that? Every time it hits you
parlay back. Your hit rate becomes 30 percent of 30 percent — nine percent. …
Now, what do you get back? … You bet $2 you get back $8 — four times what you
started with. So, if you bet it back again, you get back $32. So, if we multiply
nine percent times $32 what we get is $2.88 for a [$2] net.
“So, by parlaying we’ve actually changed the advantage,” Dave
concluded.
Well, kinda-sorta… but more on that later.
While the esteemed Mr. Schwartz was talking betting strategy,
I was opining that a horseplayer can — and often does — eliminate his advantage
by wagering outside of his core competencies. In other words, if a player has
an established Kelly
edge of, say, five percent betting to win, it cannot be assumed that he will
retain that edge betting an exacta or a trifecta or some other type of non-win wager.
“My take on folks who are trying to increase their
advantage is that they’re not going to [try to] increase it using their area of
expertise,” I argued.
Referring to Dave’s example of the 30 percent win bettor with
the 20 percent ROI, I said: “The average player, in my mind, is not going to
look at that and think, ‘well, I’m going to parlay this.’
“… They’re going to bet a pick-3. And betting a pick-3
and betting a parlay — even though they’re often compared to show you what a great
deal a pick-3 is — is not the same thing, because you start betting multiple
horses.
“[Likewise], somebody that thinks, ‘you know what? $8, a
20 percent ROI — that’s nothing! I don’t want it,” I continued. “… So, they’re
gonna play the exacta, they’re gonna play the trifecta … now, you don’t know what your advantage is. … And my
argument to you … is that you can take a positive and turn it into a negative.
And that’s exactly how you do it, by playing other areas; basically, not using
your core competencies in a proper manner.”
At that point, Dave said I was “wrong” and a bloody
battle ensued, killing thousands and literally changing the landscape of
Colorado (where I live) and Nevada (where Dave resides)… OK, not really, but we
did have a great discussion about wagering strategies and money management
techniques, which I want to further expound upon here.
First of all, it needs to be pointed out that “money
management” means different things to different people. I have often noted that
many horseplayers seem to confuse it with handicapping. To me, “I knew I should
have used that horse” is not a money management issue — it is a handicapping
issue. That said I was surprised that, given our combined experience playing
the races, Dave and I could not agree on a definition.
Secondly, there is a lot of subtlety involved in betting
strategies, as demonstrated by Dave’s straight win bet vs. parlay example. Dave
noted that “by parlaying, we’ve actually changed the advantage,” which, on the
surface, is true.
However, that “truth” rests on the supposition that:
A) ROI and “advantage” are one and the same (I don’t think they are which I will discuss later).
A) ROI and “advantage” are one and the same (I don’t think they are which I will discuss later).
B) The parlay is viewed as one bet, which it definitely is
not. In fact, a two-horse parlay consists of 1-2 bets — one, if the first horse
loses; and two (with a higher stake), if the first horse wins. It is the higher
stake, or bet amount, that leads to the higher ROI.
To demonstrate what I mean, take a peek at the following
table:
 |
| (Click on image to enlarge) |
Notice that when we parlay, we are actually investing more money. Hence, the theoretical 44 percent ROI that Dave alluded to equates to just 5.9 percent in practice. (For the financially savvy among you, this is similar to the difference one sees when comparing a simple interest rate to a compound interest rate.)
Given this, it should come as no surprise that, using a
similar bankroll, a player adept at win betting — which is what the 30 percent
wins, 20% ROI tells us — is much better off betting an equal amount to win on all
of her selections. Whereas a parlay returns just $576 on $544 bet (a profit of
$32), straight win betting yields $652 on that same $544 (a profit of $108).
Again, I realize the distinction here is subtle. I’m sure
many will argue that the parlay is a
single bet and, therefore, more profitable. But if we accept that, it’s only
fair to look at other staking methods. And, despite its flaws, the Kelly
Criterion is still numero uno when it comes to optimizing one’s bankroll:
OPTIMAL AMOUNT OF BANKROLL BET = WIN RATE – LOSS RATE / AVG. WINNING ODDS
OPTIMAL AMOUNT OF BANKROLL BET = WIN RATE – LOSS RATE / AVG. WINNING ODDS
Not surprisingly, when we plug in our straight wagering
and parlay averages from above, we get decidedly different Kelly advantages:
Straight Win Bets: 0.30 – 0.70 / 3 (odds) = 6.7 percent.
Parlay Bets: 0.09 – 0.81 / 15 (odds) = 3.6 percent.
Once more, these differing percentages point to the
delicate balance between risk and reward present in all forms of gambling and
the nuance involved in optimizing one’s results.
And that’s something I know Dave and I can agree on.
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