The cheapest way to get one, is to buy one, actually. Other ways are more expensive.

Buying heats is the 2nd place in price way; heats are cheaper than existing leopons and tigons, but you need to get lucky OR buy several before you actually get one born, chance of it passing is very low. You might need so many heats it'd cost more than buying one outright.

Trying for a G1 with mass-breeding CRBs is the most expensive way. You will need to use hundreds of GB to buy CRBs for it, and I mean hundreds - from personal experience, I used over 300 by now, never got any hybrids.
Mass-breeding without CRBs, the chance of getting a hybrid is too low. Like winning a car from a lottery low. It might never happen with thousands and thousands of lionesses, so its not a reliable way to get one; its so rare you might just never get it.

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if you can't afford to buy one, you could mass breed (and maybe use crbs) hoping for a g1, or buy heats.

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