Horses Better At Adding Than Some Humans

A study from Germany suggests that horses may be more mathematically inclined than originally thought. Researchers from the University of Gottingen trained three Shetland ponies to choose images that matched a specific visual cue.

First Drs. Vivian Gabor and Martina Gerken taught the ponies to walk up to a device and press a button; they were rewarded each time they approached the device and eventually for pressing one of the buttons.

Next, the ponies were shown a computer screen on the device that had a stimulus image in the center, and two images below it—one of which matched the stimulus. Each time the pony touched the image that matched the stimulus image, he got a treat delivered through a tube. To make sure the ponies weren't just selecting a familiar symbol, the researchers changed the options on the computer screen each time.

Once the ponies learned this, the scientists ran the same test, but used different quantities of the same image. For example, the stimulus image may show two dots; the options below may show two options: one with two dots and one with three. If the ponies chose the two-dot choice, they got a treat.

The researchers varied the size and arrangement of the images to ensure the ponies were choosing options based on numbers alone and not on other visual cues. The final phase of the study used images that were groupings of different geometric symbols, such as a cross, triangle and rhombus.

All three ponies had an 80 percent accuracy in matching images with at least four elements in at least two training sessions. One pony could tell the difference between four and five geometric symbols.

While proving that a horse's cognitive abilities may be much higher than previously believed, these finding don't mean the pony was “counting,” the team says. True counting indicated that the individual had an idea of numerical order. The ponies were subitizing: Quickly and spontaneously adding a short number of objects. Some primates and avian species can do this.

Read more at EQUUS magazine.

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A.P. Indy: Destined for Greatness

Editor's note: A.P. Indy died Feb. 21, 2020, at age 31 due to the infirmities of old age at Lane's End in Versailles, Ky. A.P. Indy was seemingly born to greatness. He was sired by Seattle Slew, a Triple Crown winner. His successful dam (mother), Weekend Surprise, was no surprise because she was sired by Secretariat, another Triple Crown champion.

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Casino Games And Mathematics. Part One.

Can the knowledge of mathematics help a gambler to win?

One can often hear that the best piece of advice given by a mathematician to a lover of gambling games is an assertion which lies in the fact that the best strategy in gambling games is complete abstention from participation in them. A lot of mathematicians consider that the most which the theory of probability and the theory of games can give a gambler are the strategies following which he won’t lose too much.

It is difficult to predict whether the American mathematician Edward Thorp shared this view, when once spending winter holidays in Las-Vegas, he, having entered a casino, decided to try his luck in the game of twenty-one. As it turned out, “Dame Fortune” was extremely unkind to him. We do not know for sure what amount of money this teacher of mathematics of one of American universities lost that winter night at the end of the 50-s – the beginning of the 60-s of the last century, however, judging by the following events the amount was not small. Otherwise, how can we account for the fact that development of an optimal strategy of this game became for a number of years an “idte fixe” of our hero. Besides, the matter was not only in the quantity of money lost by the mathematician. Perhaps, Thorp was simply an extremely venturesome person, and his pride both of a gambler and an expert-mathematician was hurt. Besides, he could suspect a croupier of dishonesty, since, as he had noticed, cards were not shuffled after each game. Though, during the game itself it did not make him very uneasy. However, afterwards, having visited casinos a number of times, he noticed that as the rules did not presuppose obligatory shuffling of cards after each game, so it was difficult to accuse a croupier of anything. Anyway, he managed to develop a winning strategy in the game of twenty-one.

This strategy among other things was based on the same very aspect which had put a defeated mathematician on his guard – cards were not shuffled too often. At that, this, apparently, as a rule, was done not because of some evil design, but in order to avoid, so to say, unnecessary slowdowns in the game. The results of his studies Edward Thorp put forth in a book published in 1962 (Thorp E.O Beat the dealer. A winning strategy for the game of twenty one. – New York: Blaisdell,1962.) which made owners of gambling houses in the state of Nevada essentially change the rules of the game of twenty-one. But let’s not ride before the hounds.

In accordance with the game rules of twenty-one of that time one croupier dealt gamblers two cards each out of a thoroughly shuffled pack consisting of 52 cards. Gamblers themselves did not show their cards to a dealing croupier. At the same time out of two cards taken for himself an official of a casino showed one of them (usually the first one) to gamblers. Gamblers evaluate their cards according to the following scale. Jacks, queens and kings have a value equal to 10 points, an ace could be assigned either 1 point or 11 points, the value of the rest of the cards coincided with their numerical value (eights had 8 points, nines took 9, and etc). That gambler was considered a winner who had cards on hand with the sum of points closest to 21 from the bottom. At that, having assessed the received cards every gambler (including a croupier) had a right to take from a pack or putting it simpler, take a “widow”, any amount of cards. However, if, as a result, the total number of points after a widow, will exceed 21 points then a gambler must drop out of a game having shown his cards.

Special rules were established with regard to stakes. Initially, upper and lower bounds were set, and every gambler had a right of choice of a specific stake (within these bounds) depending on the evaluation of his position. If, as a result, it turned out that in accordance with the game rules a casino’s visitor had a “better” number of points on hand than a croupier had, he received a gain in the amount of the stake that he had made, otherwise, this gambler lost his stake. In case of an equal number of points of a gambler and a croupier, the game ended in peace, that is the result of the game is considered “harmless” both for a gambler and a casino.

Let’s point out that unlike ordinary gamblers a croupier is not obliged to open his cards in that case if the number of points in these cards exceeds 21. Moreover, after all the gamblers have opened their cards, and therefore, all the stakes go to a casino gamblers cannot practically find out what was the number of points of a croupier, in order to build their game strategy for the next game (whether to risk or not to stand pat, and etc). It goes without saying, it gives a croupier considerable advantages. Besides, all the gamblers are surely aware of this, and, … continue to play. Nothing can be done about it, who does not take risks, as is known, does not win.

Japan Rules The Roost, Again, In Hong Kong

by Alan Carasso

Twelve months after supplying three of the four winners of the Longines Hong Kong International, the six-strong team from Japan accounted for two of the Group 1 events Sunday at Sha Tin Racecourse, as Normcore (Jpn) (Harbinger {GB}) took out the G1 Longines Hong Kong Cup beneath substitute jockey Zac Purton and Danon Smash (Jpn) (Lord Kanaloa {Jpn}) followed in the hoofprints of his dual G1 Longines Hong Kong Sprint-winning sire with a rare foreign victory in the 1200-meter dash. Ryan Moore put a peach of a ride on Danon Smash one race after guiding Mogul (Ire) (Galileo {Ire}) to a commanding defeat of Exultant (Ire) (Teofilo {Ire}) in the G1 Longines Hong Kong Vase. The locals did not leave empty-handed as Golden Sixty (Aus) (Medaglia d’Oro) turned in his customary stretch rally to blow away his rivals in the G1 Longines Hong Kong Mile, his 11th straight victory and 14th in 15 career outings. The Mile marked the end of the line for two-time winner and Horse of the Year Beauty Generation (NZ) (Road to Rock {Aus}), who is to be retired to Living Legends in Australia following a creditable fifth-place effort. Full reports of each of the four Longines Hong Kong International Races to follow.

Sunday, Sha Tin, Hong Kong
LONGINES HONG KONG CUP-G1, HK$28,000,000 (£2,719,596/€2,982,832/A$4,816,012/US$3,612,093), Sha Tin, 12-13, 3yo/up, 2000mT, 2:00.50, gd.
1–NORMCORE (JPN), 122, m, 5, by Harbinger (GB)
1st Dam: Chronologist (Jpn), by Kurofune
2nd Dam: In This Unison (Jpn), by Sunday Silence
3rd Dam: Rustic Belle, by Mr. Prospector
(¥22,000,000 Ylg ’16 JRHAJUL). O-Seiichi Iketani; B-Northern Racing; T-Kiyoshi Hagiwara; J-Zac Purton; HK$15,960,000. Lifetime Record: G1SW-Jpn, 17-7-1-3, HK$43,466,640. *1/2 to Chrono Genesis (Jpn) (Bago {Fr}), MG1SW-Jpn, $5,245,766. Werk Nick Rating: F. Click for the eNicks report & 5-cross pedigree.
2–Win Bright (Jpn), 126, h, 6, Stay Gold (Jpn)–Summer Eternity (Jpn), by Admire Cozzene (Jpn). O-Win Co. Ltd; B-Cosmo View Farm; T-Yoshihiro Hatekeyama; J-Masami Matsuoka; HK$6,160,000.
3–Magical (Ire), 122, m, 5, Galileo (Ire)–Halfway to Heaven (Ire), by Pivotal (GB). O-Derrick Smith, Mrs John Magnier & Michael Tabor; B-Orpendale, Chelston & Wynatt; T-Aidan O’Brien; J-Ryan Moore; HK$2,800,000.
Margins: 3/4, NO, 1 1/4. Odds: 9-1, 9-1, 19-10.
Also Ran: Danon Premium (Jpn), Furore (NZ), Dances With Dragon (NZ), Skalleti (Fr), Time Warp (GB). Click for the HKJC.com chart, PPs and sectional timing. VIDEO. Click for the free Equineline.com catalog-style pedigree.

Sunday, Sha Tin, Hong Kong
LONGINES HONG KONG MILE-G1, HK$25,000,000 (£2,426,394/€2,662,282/A$4,299,260/US$3,225,227), Sha Tin, 12-13, 3yo/up, 1600mT, 1:33.45, gd.
1–GOLDEN SIXTY (AUS), 126, g, 5, by Medaglia d’Oro
1st Dam: Gaudeamus (GSW-Ire, $179,846), by Distorted Humor
2nd Dam: Leo’s Lucky Lady, by Seattle Slew
3rd Dam: Konafa, by Damascus
1ST GROUP 1 WIN. (A$120,000 Ylg ’17 MMGCYS; NZ$300,000 2yo ’17 NZBRTR). O-Stanley Chan Ka Leung; B-Asco International Pty Ltd (Qld); T-Francis Lui; J-Vincent Ho; HK$14,250,000. Lifetime Record: Ch. 4yo-HK, 15-14-0-0, HK$52,845,600. *1/2 to Igitur (Aus) (Helmet {Aus}), SP-Aus. Werk Nick Rating: A+++ *Triple Plus*. Click for the eNicks report & 5-cross pedigree.
2–Southern Legend (Aus), 126, g, 8, Not A Single Doubt (Aus)–Donna’s Appeal (Aus), by Carnegie (Ire). (A$280,000 Ylg ’13 INGEAS). O-Boniface Ho Ka Kui; B-Corumbene Stud (NSW); T-Caspar Fownes; J-Karis Teetan; HK$5,500,000.
3–Admire Mars (Jpn), 126, c, 4, Daiwa Major (Jpn)-Via Medici (Ire), by Medicean (GB). (¥52,000,000 Ylg ’17 JRHAJUL). O-Junko Kondo; B-Northern Farm; T-Yasou Tomomichi; J-Ryan Moore; HK$2,500,000.
Margins: 2, NK, NK. Odds: 3-10, 30-1, 22-5.
Also Ran: Waikuku (Ire), Beauty Generation (NZ), Order of Australia (GB), Mighty Giant (NZ), Ka Ying Star (GB), Simply Brilliant (GB), Romanised (Ire). Click for the HKJC.com chart, PPs and sectional timing. VIDEO. Click for the free Equineline.com catalog-style pedigree.

Sunday, Sha Tin, Hong Kong
LONGINES HONG KONG SPRINT-G1, HK$22,000,000 (£2,135,036/€2,341,961/A$3,783,349/US$2,838,187), Sha Tin, 12-13, 3yo/up, 1200mT, 1:08.45, gd.
1–DANON SMASH (JPN), 126, h, 5, by Lord Kanaloa (Jpn)
1st Dam: Spinning Wildcat, by Hard Spun
2nd Dam: Hollywood Wildcat, by Kris S.
3rd Dam: Miss Wildcatter, by Mr. Prospector
O-Danox Co Ltd; B-K I Farm; T-Takayuki Yasuda; J-Ryan Moore; HK$12,540,000. Lifetime Record: MGSW & MG1SP-Jpn, 22-10-3-1, HK$44,645,990. Werk Nick Rating: A+++ *Triple Plus*. Click for the eNicks report & 5-cross pedigree.
2–Jolly Banner (Aus), 126, g, 9, Lonhro (Aus)–Valkyrie Diva (Aus), by Jade Robbery. (A$300,000 Ylg ’13 INGEAS). O-Mr & Mrs Kenny Cheng Tsin Ki; B-Makybe Racing & Breeding (Vic); T-Ricky Yiu; J-Mickael Barzalona; HK$4,840,000.
3–Rattan (NZ), 126, g, 7, Savabeel (Aus)–Grand Princess (Aus), by Last Tycoon (Ire). (NZ$150,000 Ylg ’15 NZBJAN). O-Wong Ting Bor; B-M H S & S H R Davidson & Mrs M P Schick; T-Richard Gibson; J-Chad Schofield; HK$2,200,000.
Margins: HF, NK, NO. Odds: 21-1, 83-1, 22-1.
Also Ran: Wishful Thinker (Aus), Fat Turtle (Aus), Computer Patch (Aus), Hot King Prawn (Aus), Voyage Warrior (Aus), Amazing Star (NZ), Stronger (Aus), Classique Legend (Aus), Big Party (Aus), Tower of London (Jpn), Big Time Baby (Ire).
Click for the HKJC.com chart, PPs and sectional timing. VIDEO. Click for the free Equineline.com catalog-style pedigree.

Sunday, Sha Tin, Hong Kong
LONGINES HONG KONG VASE-G1, HK$20,000,000 (£1,941,120/€2,129,056/A$3,438,840/US$2,580,090), Sha Tin, 12-13, 3yo/up, 2400mT, 2:27.21, gd.
1–MOGUL (GB), 121, c, 3, by Galileo (Ire)
1st Dam: Shastye (Ire) (SP-Eng), by Danehill
2nd Dam: Saganeca, by Sagace (Fr)
3rd Dam: Haglette, by Hagley
(3,400,000gns Ylg ’18 TATOCT). O-Michael Tabor, Derrick Smith & Mrs John Magnier; B-Newsells Park Stud; T-Aidan O’Brien; J-Ryan Moore; HK$11,400,000. Lifetime Record: G1SW-Fr, GSW-Eng & Ire, 11-5-1-1, HK$15,723,660. *Full to Secret Gesture (Ire), GSW & MG1SP-Eng, G1SP-Ger & Fr, GISP-US, $746,427; Maurus (GB) (Medicean {GB}), MSW & MGSP-Aus, $510,297; Sir Isaac Newton (GB), GSW-Ire, SW-Eng, GSP-Aus, $405,120; Japan (GB), Hwt. 3yo-Eng & Ire at 9.5f-11f & 11-14f, Hwt. 3yo-Eur at 9.5-11f, G1SW-Eng & Fr, $2,039,233. Werk Nick Rating: A. Click for the eNicks report & 5-cross pedigree.
2–Exultant (Ire), 126, g, 6, Teofilo (Ire)–Contrary (Ire), by Mark of Esteem (Ire). O-Eddie Wong Ming Chak & Wong Leung Sau Hing; B-Ballygallon Stud; T-Tony Cruz; J-Zac Purton; HK$4,400,000.
3–Columbus County (NZ), 126, g, 5, Redwood (GB)–Spirit of Sandford (NZ), by Kilimanjaro (GB). (NZ$33,000 Ylg ’17 NZBFEB). O-Mr & Mrs Hamen Fan Shi Hoo, Alex Fan Chen Yen & Christina Fan Chen Mun; B-D W Mayers & Mrs S J Taylor; T-Caspar Fownes; J-Joao Moreira; HK$2,000,000.
Margins: 3, HF, 2HF. Odds: 8-5, 7-10, 13-2.
Also Ran: Ho Ho Khan (NZ), Playa del Puente (Ire), Chefano (SAf), Royal Julius (GB). Click for the HKJC.com chart, PPs and sectional timing. VIDEO. Click for the free Equineline.com catalog-style pedigree.

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