21 Stud

My latest video from the 2022 Table Game Protection and Table Games Conference is 21 Stud.


Direct: https://www.youtube.com/watch?v=QDhXo1-w5wQ

This game is blackjack with NO decision making. Your initial two cards are all you get.

In addition:

1. Ace-Ace counts as a blackjack
2. Player wins blackjack ties
3. Dealer wins all other ties

I found the game creator, Brandon Zyxnfryx, to be quite delightful.

The question for the poll is would you play 21 Stud? (multiple votes allowed)

Using an infinite deck approximation, I calculate the House Edge of 21 Stud to be 0.068170977, or 6.817%. I did assume that the BJ (A-A) payout was 1.5 when dealer also has a blackjack.

BTW, is Brandon Zyxnfryx related to Mr. Mxyzptlk?

Quote: gordonm888

Using an infinite deck approximation, I calculate the House Edge of 21 Stud to be 0.068170977, or 6.817%. I did assume that the BJ (A-A) payout was 1.5 when dealer also has a blackjack.

Here is a summary of my infinite-deck analysis.

Event	Pays	Probability	Return
Player BJ win	1.5	0.050418	0.075628
Dealer BJ win	-1	0.050418	-0.050418
BJ tie	1.5	0.002836	0.004254
Other win	1	0.413781	0.413781
Other Loss	-1	0.413781	-0.413781
Other tie	-1	0.068765	-0.068765
Total		1.000000	-0.039302

Quote:

BTW, is Brandon Zyxnfryx related to Mr. Mxyzptlk?
link to original post

Good question, but I didn't ask.

Oh, I had assumed that A-K was not a blackjack (and thus paid 1-1 and lost to Dealer A-A) because A-A was defined to be a blackjack.

Making that correction, my calculation is now HE = 0.03937541 or -3.9375% However, my calculation is actually a 6-deck calculation in which the dealer hand probabilities are insensitive to the two cards in the players hand.

So, I repeated this calculation based on a 600 deck shoe and I get a House Edge of -0.03930257, which is close enough to confirm your infinite deck result.

Nice game. I would trial it. I'd probably want to find a way to reduce the house edge a tiny bit, but not as low as BJ because you can't misplay hands.

Solid game and play. Easy to learn. Not intimidating for women or new players in general because their play does not affect others. Nice side bet paytable with a possibility to add a progressive for either both cards matchimg or 4 card poker hands.

Well done.


ZCore13

Event	Pays	Probability	Return
Player BJ win	1.5	0.050418	0.075628
Dealer BJ win	-1	0.050418	-0.050418
BJ tie	1.5	0.002836	0.004254
Other win	1	0.413781	0.413781
Other Loss	-1	0.413781	-0.413781
Other tie	-1	0.068765	-0.068765
Total		1.000000	-0.039302

This game looks incredibly countable

Welcome to the forum, cosmiccow. Its always a good idea for newcomers to take a look at the rules: Forum Rules We look forward to getting to know you!

I think the question of countability is To Be Determined. Yes, a high frequency of getting BJs is in the player's favor, so Aces and (to a lesser extent) Tens should have a positive EOR. But I suspect that excess Tens may also increase the probability of player and dealer tieing on non-BJ hands, and that is where the dealer's advantage comes from. I would normally calculate EORs for the ranks, but I'm about to be very busy for a week, so I imagine some others will do it. This is an easy game to analyze.

Most of my profit in BJ comes from Double Downs, Splits, and Black Jacks. Maybe I cut my losses a bit with surrender too.
Where's the bright points of winning in this game?

Quote: ChumpChange

Most of my profit in BJ comes from Double Downs, Splits, and Black Jacks. Maybe I cut my losses a bit with surrender too.
Where's the bright points of winning in this game?
link to original post

That's kind of where I'm at. The lack of player decision makes it approachable, but not enjoyable. I got a chance to play this at the show and I found the side bets to not be engaging enough to make up for no strategy.

It has a place on the casino floor, but it's not something I'd want to play.

Quote: SphinxOfCups

It has a place on the casino floor, but it's not something I'd want to play.
link to original post

Edited. Replied to wrong post in this one. Deleted.


ZCore13