Pick 5 or Empire 6? (1436 Views)

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**Mathcapper** (IP Logged)

Date: August 31, 2019 12:33AM

As we approach the end of the Spa meet with another mandatory payout day coming up, I thought it’d be worthwhile to take a look at the value of the Empire 6 bet, both independently and vis-à-vis the Pick 5.

Seeing as we’re less than 20 race days into the launch of the new bet, it’s still far too early to make any statistically significant conclusions, but I’m already seeing the expected tendencies in the Empire 6, and to an even greater degree.

Excluding the mandatory payout day earlier in the meet (which paid +400% more than the takeout-adjusted win parlay), the median payout has been +145% more than the takeout-adjusted win parlay.

To put that in perspective, as I noted in a post on the subject of the Rainbow 6 a few years ago, the median payout over 10 meets (290 days) I tracked of traditional non-carryover Pick 6’s on the NYRA and SoCal circuits was +27% higher than the win parlay. On carryover days, it jumped to +78% higher than the win parlay. And in the 158 days I tracked of the Rainbow 6, it was +98% higher.

At almost two and a half times the win parlay, the Empire 6 is currently paying better than all of them. Much of this is likely due to the same phenomenon we see in the Rainbow 6 (players spreading too deep, driven by both the $.20 minimum and their attempt to capture the jackpot, “sharpies” shunning the bet due to the perceived takeout disadvantage, etc.).

During the same timeframe since the Empire 6 began at the Spa, I also tracked the payouts for the Pick 3, Pick 4 and Pick 5 within the Empire 6 sequences. The median Pick 3 payout was +24% more than the equivalent win parlay, the median Pick 4 payout was +60.4% higher, and the Pick 5 was +123% higher.

So which bet is offering the best value?

To answer that question, we first need to take a look at how much each bet SHOULD pay. In general, the more legs involved in the sequence, the better the value is going to be, because you’re only getting hit with the takeout ONCE, and because you edge is multiplicative. But differences in the takeout between the various bets must also be taken into consideration, which can reduce or increase the value of the particular bet.

Let’s look at the expected value in each bet, after taking into account both of these factors.

The Pick 3 has a takeout of 24%, but because you’re only getting hit with that takeout one time in the sequence vs. three times at 16% in the win pool, the Pick 3 should, on average, pay +28.2% more than the equivalent win parlay.

Similarly, the Pick 4, which also has a 24% takeout, should pay on average 52.7% more than the equivalent win parlay, again, because you’re only getting hit with the takeout once.

The Pick 5 is even better, both because it has an industry-low takeout rate of only 15% and because you now have five legs where you’re only getting hit with the takeout once. As a result, the Pick 5 should on average pay +103% (more than double) the equivalent win parlay.

The Empire 6, another one of the often-derided jackpot bets, is subject to a much higher effective takeout than the Pick 5. With its initial 20% takeout, along with the additional 25% takeout for the jackpot pool, players are looking at an effective takeout of (1-0.8*0.75) = 40%. As I wrote about in my Rainbow 6 post, this may seem quite onerous, but when you compare it to the traditional Pick 6, which has a similar “takeout” for 5-of-6 consolation bets that get paid out to mostly non-winners of the Pick 6, an argument can be made that it’s close to a wash, and the evidence has been that’s it’s actually much better, for the reasons stated earlier.

In any event, the Empire 6, because you’re now looking at six legs where you’re only facing the takeout once, should pay on average +70.8% more than the equivalent win parlay.

All in all, just looking at it mathematically, the Pick 5 currently offers the better value than the Empire 6 (+103% vs. +70.8%). Not a surprise, given the 15% takeout vs the effective 40% takeout in the Empire 6, albeit mitigated by the inclusion of the extra leg in the Empire 6.

However, a mathematical interpretation doesn’t give us the full picture. When we look at what the bets are *actually* paying, we see differences to what the math is predicting. In the jackpot wagers, as we’ve seen with the Rainbow 6 and now with the early results for the Empire 6, the bet is paying much higher than predicted, likely for the reasons stated earlier.

So while the math is saying that the Pick 5 offers the better value (+103% vs. +70.8%), the actual results are saying that the Empire 6 is a slightly better bet (+145% vs. +123%). A couple of caveats though: (1) the sample size is still way too small and (2) the Rainbow 6, a similar bet to the Empire 6, was shown in a longer study to pay “only” +98% more than the parlay, so it’s quite possible, indeed likely, that the +145% initial early average will come down somewhat over time.

Another factor I should briefly touch upon relates to recent discussions about whether or not the computer guys are being kept out of the Pick 5. This may or may not be true, but the supposition is that if they are being kept out, we may see higher-than-expected payouts in the Pick 5 relative to the other horizontal exotics. It’s too early to tell, but based on the results above, the Pick 5 is offering better value than the Pick 4 and Pick 3 relative to expectations (+123% vs. +103% expected for the Pick 5, +60.4% vs. +52.7% expected for the Pick 4, and +24.2% vs. +28.2% for the Pick 3).

Again, the sample size is way too small right now to draw any conclusions. Day-to-day variations still have too much impact on the overall results, like today for instance where the Pick 3 paid +3.1% more than the win parlay and the Pick 4 paid -19.4% less than the win parlay but the Pick 5 paid a whopping +345% more than the win parlay, most likely driven by Remain Anonymous, the 15-1 ML firster in the first leg of the Pick 5 that got pounded to 5-2 in the win pool (6-1 in the Will Pays).

Over time, I’d expect the Pick 3, Pick 4 and Pick 5 payouts to converge on their mathematical expectations, unless the computer guys are indeed being excluded from the Pick 5, in which case it’s possible we see a little extra value in the wager (although not a certainty). The Empire 6 is another matter. Based on the previous studies related to similar wagers, I’d expect the bet to continue to provide more value than the mathematical prediction, albeit probably less than what may be a somewhat inflated +145% figure we’re seeing in the early going.

Until such time that we’ve gathered enough results, the jury’s still out on whether the Pick 5 or the Empire 6 offers the better value. Whichever the case, they both appear to be two of the best bets in racing, aside from the jackpot mandatory payout day and barring any introduction of a traditional pick 6 with a 15% or 20% takeout with NO jackpot and NO 5-of-6 consolation tickets (one can only wish).

Good luck everyone in Monday’s mandatory.

Looking forward also to Penn Derby day down at Parx and to seeing fellow T-Generates like Joe B. and any cameos from other members of the backyard crew.

Rocky R.