adding joker - increase in expectation

6 deck. one joker added. joker can be used as any card if received by player. if dealer gets joker, it is burned.

1. what is the increase in ev over baseline condtions?
2. does the benefit decrease as a function of players at table or is it about the same on a per hand basis?

My rough estimate was an additional 0.6% advantage to the player at the start of the shoe, increasing linearly as cards are removed (and the chance of getting joker increases) until joker is played, and then there is no advantage after joker played (until shuffle).

I Estimated the benefit to player (increased expection) on the first hand after shufle = probability of getting joker x the benefit gained by getting joker on single hand.

I figure chance of getting joker on first card = 1/313. same for getting joker on second card. if the joker gets paired with an ace or 10, it is an automatic increase in expectation of 1.5 (since payout is 1.5). Benefit is less profound with a 2-9 where I would use the joker to turn in into an 11. gets a little more complicated trying to figure if joker occurs after the first 2 cards received.

Anyone else come across something like this or able to make reasonable approximations?

SW in Basic Blackjack says that adding a joker as card of your choice in a six decks game adds+0.7% to expectation. He has a detailed strategy for playing a hand with a joker.

You ignore the case where you get the joker as a hit card.

I tried wizard of odds and a bunch of other sites, but did not think of wong's book. I have professional blackjack but not basic blackjack.
Shouldn't strategy be pretty obvious?
If paired with a 10, wild card turns to ace. w/ ace, wc = 10, w 2-8, whatever it takes to get 11. w/ a 9, wc = A. the only I have to think about is an 8- is an 8/3 better than A/8- I guess it would depend on dealers upcard.

"the only one I have to think about is an 8-. Is an 8/3 better than A/8? I guess it would depend on dealer's upcard."

8,3 better except for dealer upcards of 7, 8, and 9.

Don

if the joker is worth 0.7% in ev in a 6 deck, I am thinking it would be comparable to a true count of about 1.2 (every plus one worth about 0.5) so I am thinking of just calling the joker as worth about +8 on a 6 deck running count. I start the running count at +8 for the first hand of the shoe and subtract 8 when joker played.

This joker count would be superimposed on a regular high low.

Does that sound like a reasonable system or would it be better to just play and go to the restroom every time the joker gets burned?

There's a saying that "expectation isn't everything." While the joker may have the added value in e.v. that you reference, that e.v. is added with greater variance involved, as there will be many doubles and naturals as a result of using the joker.

So, its effect on the game isn't identical to simply having a higher count, in the traditional sense.

The same is true as when you attempt to calculate the optimal bet for when you know you will have an ace in your original hand. It gives you a huge 52% edge, but when calculating the optimal wager, you need to tone it down somewhat, because so many of the hands result in naturals, which add to variance.

Don

this is a $200 max bet - and $100 max if they do not have the "high limit" table open.
So even 2 x $200 max is <<<1% of my bankroll. So I don't think I need to be especially concerned about the variance.

If you start your count at +8 and deduct the +8 from the count when joker is out , you would be betting your advantage correctly but you need to reduce your running count by 8 (before the joker appears) for playing your hands correctly.

I think I will just use hi low and remember when joker played. All breaks and table hops will be after joker is out