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Remember when you thought I was dumb yesterday

So do you decide whose mulliganning first based on who has drawn the most lost souls? Because whether or not my opponent mulligans may make me change my mind.

I wasn't really thinking about it, but that makes sense to me.

So do you decide whose mulliganning first based on who has drawn the most lost souls? Because whether or not my opponent mulligans may make me change my mind.

 I would think the player with the most lost souls in territory has the first option to mulligan. Just like when you begin the game.

I just ran a Monte Carlo for the Olijar strategy (i.e., take a free mulligan whenever you draw any number of Lost Souls). Frankly it is disastrous.  Over 75% of games would start with at least one player having no lost souls available for rescue.

Oh well...

Can confirm. For a comparison, with no mulligan, approximately 40% of the games start with at least one player not drawing a lost soul. That's a fairly large difference. Interestingly, for a 56 card deck, these numbers are only slightly higher for a 56 card deck.

I think the decision should take into consideration the added complication to the game, the time it takes away from play in tournaments, and the fact that it potentially lengthens the average game time.
Is the added complication of a mulligan worth it? I know it's not much, but it does add one more layer to the game and makes it ever so slightly out of the reach of understanding for younger/newer players. It probably is, I'm just tossing that out for thought :-)

The player who has drawn the most souls gets to choose whether to Mulligan first. A player can choose to mulligan one time per game. All souls drawn stay out. The entire hand is shuffled and the player draws 8, replacing souls as necessary.

If this is adopted, I would encourage this with the modification that they draw one less than before.

It's silly to punish people for bad luck, but it still deters people from attempting to trade an average hand for a good one, by threatening additional soul draw. I don't think there's a single good reason that Lost Souls should be put back in the deck.

I see it more as a consideration/calculation of risk vs. reward. Unless we allow people to pick their opening hand, there's always going to be a risk of drawing a combination of lost souls and weak defense. If you want to mitigate that, play closer to heroless or herolite. Luck of the draw is part of the fun of the game. If we mess with that, it sure feels to me like there should be greater risk than just possibly drawing more Lost Souls - i.e. draw fewer cards.

Remember when you thought I was dumb yesterday

Yesterday was more like further confirmation.

i may be crazy but i have more nats titles than westy

Yeah but that was booster draft, so it doesn't really count.

I know I'm a little late to this conversation but what about this option:

If the player chooses to mulligan then they set aside their hand face up, shuffle all souls into their deck, draw a full replacement hand, choose whether or not to mulligan again, (if yes then repeat previous), then resolve lost soul abilities and lastly the opponent then places the original hand(s) on the bottom of owner's deck. 

There are a few factors that create tension here.  If you can't shuffle the lost souls back in then I don't see a point of having a mulligan.  The main reason for mulligan imo is to address those games where you draw five lost souls and no defense which leads to a very quick and boring game. It is not fun to lose or win this way.

I understand the concern about lost soul drought and players trying to abuse mulligan's to increase that.  I don't like the options of searching the deck for a soul or choosing one to leave out because I think that adds more complication to it. I also don't think drawing one less card is really helpful here. In magic that is a sufficient deterrent but in Redemption if they draw one less card then there is less chance of them drawing souls and some decks might actually like starting with less cards.

 I think my suggestion would alleviate the soul drought issue because the odds for drawing more lost souls should increase with each mulligan. So if you get three or more souls it might be worth doing the mulligan but if you only drew one soul then I doubt it would still be favorable to mulligan in hopes of getting 0.  The opponent also gets to see some of your deck and choose the order of the bottom cards which I think would be enough for players to only want to mulligan if they have a truly unplayable starting hand.

It's silly to punish people for bad luck

It is not about punishing people but if there is no significant drawback to using the mulligan then it will lead to being overused. You don't want people doing a mulligan simply because they don't have Guardian, SoG, favorite hero, fortress, etc in their opening hand. If someone wants to mulligan simply so they can get Auto to start then their should be some balancing factor to that.

Might thoughts here are only for type 1 2-player because the dynamics for multiplayer and type 2 are different and may need to be considered differently.