How much does the bullion price affect price of old gold coins?

Do swings in the price of gold affect the price of sought-after coins like Indians and Libertys? Or is the price mostly determined by scarcity, condition, and collector interest? Thanks.
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If a coin is "common" enough to sell at a fairly small premium to gold (for example, an XF 1894-S double eagle) or it exists in quantity (for example, a "common-date" MS-63 Saint), then it will be very sensitive to a fairly small change in the price of gold (say, 5%). On the other hand, a coin like an XF 1850 half eagle sells for a large enough premium over the price of gold that it would take a fairly large change in the price of gold to have an effect - gold might have to go up to $750/oz. to have an impact on the half eagle.
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<< <i>It really depends on the coin.
If a coin is "common" enough to sell at a fairly small premium to gold (for example, an XF 1894-S double eagle) or it exists in quantity (for example, a "common-date" MS-63 Saint), then it will be very sensitive to a fairly small change in the price of gold (say, 5%). On the other hand, a coin like an XF 1850 half eagle sells for a large enough premium over the price of gold that it would take a fairly large change in the price of gold to have an effect - gold might have to go up to $750/oz. to have an impact on the half eagle. >>