ilovejokers: special joker, what is it worth?

[ilovejokers]

set of rules: 6D, s17, ENHC, no surrender, NRSA, D9, DAS
casino conditions: crowded tables. set of rules like in the uk, -0.6% without joker.
in other words: shit.
They use 1 joker in the shoe: no effect on ties and losses and dealer hands. if a player gets it: (s)he is paid double if and only if (s)he wins the hand.
what may be the theoretical value? i am personally not interested in this game, but maybe there will be another at another place in the world and it might be useful to know it.
if anyone still wants to know the place i mail.

[Don Schlesinger]

> They use 1 joker in the shoe: no effect on ties and
> losses and dealer hands. if a player gets it: (s)he is
> paid double if and only if (s)he wins the hand.
> what may be the theoretical value?

Depends on how many people at the table. If you're alone, you get the joker (roughly) half the time and you win about 43% of your hands. So, 21.5% of the time, you win an extra bet. The joker is worth, therefore, 0.215%.

But, at a full table ... one quarter of that amount.

Don

[ToJeDobro]

I am misunderstanding 2 aspects of the answer regarding the joker's value. Any help would be appreciated.

1. Why wouldn't one need to adjust the 21 1/2% to reflect the number of hands per shoe? In other words, why am I wrong to calculate 1 extra bet half the time only on the 43% winning hands equals an expectation of 0.215 extra win per shoe and assuming ~58 hands per shoe (312 / (2.7cards/hand X 2 people)), my expectation is 0.215 / 58 = ~0.37% extra win per hand?

2. I'm unclear why the full table reduces the expectation to 1/4 of the amount. I see that a player would receive 1 extra bet 1/8th of the time on only her 43% of winning hands, which is 5 3/8%-which is of course 1/4 of 21 1/2%.

However, why isn't the player simply receiving on average 0.05375 extra win on approximately 14.44444 hands (312/(2.7*8)), giving an expectation of 0.05375/14.444444 = ~0.37% extra win per hand, the same as heads up?

> Depends on how many people at the table. If you're
> alone, you get the joker (roughly) half the time and
> you win about 43% of your hands. So, 21.5% of the
> time, you win an extra bet. The joker is worth,
> therefore, 0.215%.

> But, at a full table ... one quarter of that amount.

> Don

[Don Schlesinger]

> I am misunderstanding 2 aspects of the answer
> regarding the joker's value. Any help would be
> appreciated.

> 1. Why wouldn't one need to adjust the 21 1/2% to
> reflect the number of hands per shoe? In other words,
> why am I wrong to calculate 1 extra bet half the time
> only on the 43% winning hands equals an expectation of
> 0.215 extra win per shoe and assuming ~58 hands per
> shoe (312 / (2.7cards/hand X 2 people)), my
> expectation is 0.215 / 58 = ~0.37% extra win per hand?

All my analyses assume 100 hands per hour. I can't answer for every different possible speed of play. I leave that adjustment to he reader.

> 2. I'm unclear why the full table reduces the
> expectation to 1/4 of the amount. I see that a player
> would receive 1 extra bet 1/8th of the time on only
> her 43% of winning hands, which is 5 3/8%-which is of
> course 1/4 of 21 1/2%.

> However, why isn't the player simply receiving on
> average 0.05375 extra win on approximately 14.44444
> hands (312/(2.7*8)), giving an expectation of
> 0.05375/14.444444 = ~0.37% extra win per hand, the
> same as heads up?

Yes, you're right. Sorry, my reasoning was incorrect.

Don