I don't have the knowledge or resources to develop a strategy engine, but here's where logic takes me:ġ) Only use the card when you're bet is large.Ģ) The cards future value declines with every hand played (i.e. If you receive a blackjack as a result of using the mulligan, it pays the usual 2:1. However, you may continue to play your hand as normal (hit after using the mulligan unless it was used to replace a double down card). You're stuck with whatever you're dealt on the first attempt to use the mulligan. And just to clarify, you cannot 'request' a particular card. If you don't use your mulligan on the first two cards, you may use it on a hit card instead, but once you've hit, you may only replace the most recent hit card. With the mulligan, you may take one of your first two cards and replace it with the next card from the shoe. To make the tournament more fun (and tough to analyze), the hands are positive EV (notably, Blackjacks pay 2:1) However, you have the opportunity to make one hand for each round (as long as its one of the first 13 of 14) SUPER positive EV by use of a 'mulligan' card. I sometimes play in a small blackjack tournament.