Variance and unusual betting

In Europe there are games where the player has to match his bet if he wants to try to improve his initial hand (discarding some cards and replacing them with new one). This kind of betting makes math difficult. I’m trying to calculate standard deviation (variance) for such a game. Can I, if I know the standard deviation (sda) for the American style of betting (1 bet) and probability (pb) of hands not doubled, calculate comparatively accurately the sd for my case? Is the following formula a good estimation?

sd = bet + bet*(1-pb)*sda

Please, take into account that payouts are multiplied by player’s initial bet no matter if one doubles his bet.

Any advice will be appreciated.

VPRookie