Ihtimal looked a filly with a future as she took the Barrett Steel May Hill Stakes at Doncaster in striking fashion.
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Sent off the 11/10 favourite under Silvestre de Sousa, she arrived on Town Moor after winning the Sweet Solera at Newmarket, an event Godolphin have traditionally targeted with some of their best juvenile fillies.
It took time for the gaps to open for Ihtimal in this Group Two contest, but she simply took off inside the final furlong and instantly cleared two lengths away from Majeyda.
De Sousa said: "She travelled well through the race and I was quite happy with the position I had.
"I was travelling so well that if the gap hadn't come she would have opened up her own gap. I never touched her - she's just done it with her own ability. She'll strengthen up through the winter and she has a bright future."
Trainer Saeed bin Suroor said: "We just wanted to keep her nice and relaxed in the race.
"She handled the ground really well and we'll look at the Group One Fillies' Mile at Newmarket. We'll talk to Sheikh Mohammed.
"She's nice and tough filly and she'll be good for the future. She is a bit tiny at the moment, but with the engine and class she has, I think she'll be fine next year."
Godolphin racing manager Simon Crisford said: "She's got a good turn of foot, that's what the race was about and she's a very good filly.
"On this type of ground they don't normally do that. She's in very good form and will run in the Fillies' Mile next.
"Her dam is a half-sister to a French Oaks winner and she'll probably go a mile and a quarter maximum next year. She'll be given a Guineas preparation."
Of Majeyda, Crisford said: "She ran well, but was beaten by a better filly on the day. However, we might look at the Fillies' Mile for her as well."
Sky Bet cut Ihtimal's odds from 25/1 down to 12/1 for next year's QIPCO 1000 Guineas and spokesman Michael Shinners said: "Godolphin tend to use this race as a trial for their most promising fillies and the winner was well on top at the line."
Be Ready gave the Ihtimal team a double with a classy performance in the One Call Insurance Flying Scotsman Stakes.
The highly-regarded New Approach colt was sent off 13/8 favourite in what looked a hot race and he duly delivered with a three-length win over Barley Mow.
"I've always liked him, even before he ran. He's got class and he's my favourite for the future which is why I ran him first time in a Listed race at Newbury," said bin Suroor.
"I'm sure he will improve a lot for this race and the Dewhurst will be the next race."