Push 22

If a game had standard blackjack rules but was played face up and the only change would be that all bets push against a dealer's 22, except natural blackjack, what would be the house edge? Thanks

First question: when you say, "All bets push against a dealer's 22," does this include bets where the player busts?

The Wizard of Odds site quotes the effect of the Push-22 rule here:

https://wizardofodds.com/games/blackjack/rule-variations/

Push-22 is the third from the bottom on the very long table of rules variations in that link.

The effect on the players return of "All dealer busts on 22 become a push" is reported to be -6.91%

Quote: Chae

If a game had standard blackjack rules but was played face up and the only change would be that all bets push against a dealer's 22, except natural blackjack, what would be the house edge? Thanks
link to original post

Interetsing idea. You may have to clarify some rules which don't come up in normal BJ, as you do strange things versus a dealer 16 etc. For instance can you split KQ or only KK,QQ etc.? Can you double KA having split K-K? Being able to split unlike pictures can be quite useful especially as you then have 4/13 chance of getting another split opportunity.

No a bust would still be a loss

For the example you could split non like 10 cards, KQ etc. but you can not double AK.

Well, this game is a combination of Double Exposure (except with Dealer NOT winning ties) and with the Push 22 rule.

Its worth looking at the Double Exposure game analysis on WOO, although it should be remembered that Player loses all ties rather than 'Dealer Bust with 22 will tie'

https://wizardofodds.com/games/double-exposure/

Even so, the strategy tables of Double Exposure are worth studying.

One rule clarification is important: Is this Dealer Hits on Soft 17 or Dealer Stands on Soft 17?

Otherwise we assume 8D, 3:2,DOA, DAS, Resplit 3 times except for Aces?

Is this a game you are designing? Or is it being offered somewhere?

I was intrigued by this game and tried it out in my monthly cards/casino night run I run with friends. It is a really enjoyable feature when a dealer has a 16 or less, and really weird when a dealer has a strong hand and the player has a lesser but otherwise good hand. The fact that the decision is obvious and players have to hit on 19 against a dealer 20 just feels wrong, although obviously the correct play. I like the concept, but once seeing a few hands like this it lost some of its appeal for me.

I've had a very quick look at this, so lots of room for typos and mistakes, especially as I got it in the Player's favour by about 1.72% if Blackjacks pay 3/2. This assumes infinite decks, s17, one split allowed (makes the calculation easier), DAS. Not being able to split KQ etc costs about 0.14%, doubling 21 is 0.01%.
Thus I suspect they only pay even money giving a HE of 0.54%.

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Mr. Handpay describes FreeBet BJ at the start of this video. If the HA for a push on 22 is so large, the free bets are to make up for it. I haven't seen this game, but it may be one to try out if I run across it. I'd have to look up a Wizard strategy for it if he's written one up.
He describes the table limits as $1 to $25 on the Pot Of Gold bet, & $10 to $1,000 on the main bet. There's no surrender. He says the HA is around 0.5%, which makes the game playable.
After finishing watching the video, he clearly overbets and he busted out $10K in one shoe. He max bets the Pot of Gold bet at $25, but what's the sweet spot for the main bet when you're having a terrible run of cards? The Push 22 didn't feature heavily if at all this time (I think it was one hand).
Would a main bet of 15X-16X the Pot of Gold bet be appropriate? Just trying to figure out 6.9% HA - 0.5% HA = 6.4% HA, then 1/0.064 = 1/15.625
So if I find a $15 table, just bet $1 on the Pot of Gold bet for each $15 bet and I'll get my freebets.


I ran across Lucky Lee Gaming trying out Freebet BJ. They have higher limits at this table with Push 22 (11 to 1 side bet) max payout of $5K and the Pot of Gold max payout of $5K (max bet of $50). I was interested in this game until it came time to payout for the BJ and it was only 6:5. Other tables pay 3:2, so find those. Luckily a BJ pays whille the dealer pushes with a 22.

Freebet is fun. The strategy for free doulbing and splits is simple, take any you get. So it seems counterintuitive to double 9 vs A, but in essence you're being paid 2 to 1 if you win except you can only draw one card. Free splits essentially give you free hands to play. There are some changes in strategy between a "money" hand and a "free" hand; the latter only gets paid if you win, so it sometimes pays to hit more often (e.g. 17 vs 7!) It has the advtange you can't lose more than your original bet after resplits/doubles (except in some rare cases where you money double soft totals, I've never seen free 9A vs 6).

Charliepatrick, thanks for doing these calcs. I was going to do something similar, but have been too busy, I really appreciate that you took the time to do this.

Is it possible that you could quote the player EV that you calculated for:

(Stand vs Split) TT vs 13
(Stand vs Split) TT vs 14

I'm just wondering how close these decisions are. These are frequently occurring hands.

Also, I suspect that H17 is used because the PUSH 22 rule helps to make H17 better for the House (relative to S17) than it normally is.

Quote: gordonm888

The Wizard of Odds site quotes the effect of the Push-22 rule here:

https://wizardofodds.com/games/blackjack/rule-variations/

Push-22 is the third from the bottom on the very long table of rules variations in that link.

The effect on the players return of "All dealer busts on 22 become a push" is reported to be -6.91%
link to original post

According to JG's BJ switch article(6D, H17), the effect of "push on dealer 22" is -7.227%.

Quote: gordonm888

...the player EV that you calculated for:

(Stand vs Split) TT vs 13
(Stand vs Split) TT vs 14...

This uses basic principles and also agrees with my spreadsheet. It seems TT vs 14 is the closest decision; I don't know whether it changes due to finite decks if you have had a few splits.

Quote: ssho88

...According to JG's BJ switch article(6D, H17), the effect of "push on dealer 22" is -7.227%....

The rough figures (note they are for comparison/discussion as they don't allow resplits etc) I got are
S17 Push 22 : -0.536% (i.e. the House has the advantage)
S17 No Push: +7.895% (i.e. the Player has an advantage)
H17 Push 22 : -1.015%
H17 No Push: +7.520%
I'm guessing the reason for the difference being more than your figure is because of not being paid on doubles and splits when you know the dealer has a bad hand but gets away with a bust 22.

A game I am trying to design because all of our players hate "Face Up 21". There are too many rules they don't like. For example they all hate that dealer wins all ties. So, I thought a simple game could be face up with all of the standard BJ rules: Dealer hits soft 17, 6 decks, natural blackjack pays 3 to 2, split up to 4 times except with A's which can only be split once and are hit only once. If I am understanding the acronyms correctly, we allow DAS (doubling on all splits) but not DOA (we do not allow doubling on split aces).

So, I thought a possible good variation would be normal blackjack face up with the above rules but all bets push when the dealer hits and lands on 22. I was thinking that the house advantage of pushing on 22 might be enough to offset the fact that the game is played face up. Let me know if you require further clarification.
Thanks

This may help answer my questions but I will have to look closer at the figures, thanks for the info.

Quote: Chae

If I am understanding the acronyms correctly, we allow DAS (doubling on all splits) but not DOA (we do not allow doubling on split aces).

So, I thought a possible good variation would be normal blackjack face up with the above rules but all bets push when the dealer hits and lands on 22. I was thinking that the house advantage of pushing on 22 might be enough to offset the fact that the game is played face up. Let me know if you require further clarification.
Thanks
link to original post

(trimmed)

I believe the usual meanings are Double After Split and Hit Split Aces. No action on split aces is a fairly common rule; so no hitting, doubling, or resplitting - this is generally the opposite of HSA.

Some players are going to absolutely hate Push on Dealer 22, too. I do not know if those are your players.

I humbly suggest only allowing D9 (may double hard 9, 10, 11) and a natural to pay 1:1 on a face up game.

Chae,

You might run into problems using "Push 22" in your game, because Geoff Hall owns the patent on that invention, see:

https://patents.justia.com/patent/20050049025

Also, do you plan to allow insurance bets?

Dog Hand

I developed a game about 20 years ago for a company that went bankrupt. It still think it is a good game.

Imagine a traditional Blackjack variant where if you busted you would be back in the game with a total of 17. In other words, you could not bust. To purchase this option costs the player an amount equal to 20% of their bet.

A $5 bettor would pay $1 upfront and could never bust. If their total exceeded 21 they were assigned a total of 17 and could still win if the dealer busted or push if the dealer got 17. It completely changed the hitting, doubling, and splitting strategy of the game. Players could opt in to this option or opt out and play against traditional rules.

If I remember correctly I think Wizard did the math for me 20 years ago.

Quote: DRich

I developed a game about 20 years ago for a company that went bankrupt. It still think it is a good game.

Imagine a traditional Blackjack variant where if you busted you would be back in the game with a total of 17. In other words, you could not bust. To purchase this option costs the player an amount equal to 20% of their bet.

A $5 bettor would pay $1 upfront and could never bust. If their total exceeded 21 they were assigned a total of 17 and could still win if the dealer busted or push if the dealer got 17. It completely changed the hitting, doubling, and splitting strategy of the game. Players could opt in to this option or opt out and play against traditional rules.

If I remember correctly I think Wizard did the math for me 20 years ago.
link to original post

For strategy, I see you would always Hit to Hard 17 when you have a hard hand. And you would probably split more often and double down a little less.

Quote: DRich

I developed a game about 20 years ago for a company that went bankrupt. It still think it is a good game.

Imagine a traditional Blackjack variant where if you busted you would be back in the game with a total of 17. In other words, you could not bust. To purchase this option costs the player an amount equal to 20% of their bet.

A $5 bettor would pay $1 upfront and could never bust. If their total exceeded 21 they were assigned a total of 17 and could still win if the dealer busted or push if the dealer got 17. It completely changed the hitting, doubling, and splitting strategy of the game. Players could opt in to this option or opt out and play against traditional rules.

If I remember correctly I think Wizard did the math for me 20 years ago.
link to original post

For strategy, I see you would always Hit to Hard 17 when you have a hard hand. And you would probably split more often and double down a little less.

Quote: gordonm888

Quote: DRich

I developed a game about 20 years ago for a company that went bankrupt. It still think it is a good game.

Imagine a traditional Blackjack variant where if you busted you would be back in the game with a total of 17. In other words, you could not bust. To purchase this option costs the player an amount equal to 20% of their bet.

A $5 bettor would pay $1 upfront and could never bust. If their total exceeded 21 they were assigned a total of 17 and could still win if the dealer busted or push if the dealer got 17. It completely changed the hitting, doubling, and splitting strategy of the game. Players could opt in to this option or opt out and play against traditional rules.

If I remember correctly I think Wizard did the math for me 20 years ago.
link to original post

For strategy, I see you would always Hit to Hard 17 when you have a hard hand. And you would probably split more often and double down a little less.
link to original post

It has been over 20 years so I don't remember all of the strategy but I think you even hit hard 18 and you would double on some 12 & 13's.

Just a quick look, so it may be wrong as I haven't checked it at all, this is what I got (infinite decks) assuming you know dealer does not have BJ. (I haven't checked whether it's better to double 10 or split 5s, similarly whether you hit soft 18 vs 6.)

	T	9	8	7	6	5	4	3	2	A
21	St	St	St	St	St	St	St	St	St	St
20	St	St	St	St	St	St	St	St	St	St
19	St	St	St	St	St	St	St	St	St	St
18	St	H	St	St	Dbl	Dbl	Dbl	St	St	St
17	H	H	H	Dbl	Dbl	Dbl	Dbl	Dbl	Dbl	H
16	H	H	H	Dbl	Dbl	Dbl	Dbl	Dbl	Dbl	H
15	H	H	H	Dbl	Dbl	Dbl	Dbl	Dbl	H	H
14	H	H	H	H	Dbl	Dbl	Dbl	H	H	H
13	H	H	H	H	Dbl	Dbl	H	H	H	H
12	H	H	H	H	Dbl	H	H	H	H	H
11	H	H	H	H	Dbl	Dbl	Dbl	Dbl	Dbl	H
10	H	H	H	H	Dbl	Dbl	Dbl	Dbl	Dbl	H
9	H	H	H	H	H	H	H	H	H	H
8	H	H	H	H	H	H	H	H	H	H
7	H	H	H	H	H	H	H	H	H	H
6	H	H	H	H	H	H	H	H	H	H
5	H	H	H	H	H	H	H	H	H	H
10	st	st	st	st	st	st	st	st	st	st
9	st	st	st	st	st	st	st	st	st	st
8	h	h	h	st	dbl	h	h	h	h	h
7	h	h	h	h	h	h	h	h	h	h
6	h	h	h	h	h	h	h	h	h	h
5	h	h	h	h	h	h	h	h	h	h
4	h	h	h	h	h	h	h	h	h	h
3	h	h	h	h	h	h	h	h	h	h
2	h	h	h	h	h	h	h	h	h	h
X-X				X	X	X	X	X	X
9-9	X	X	X	X	X	X	X	X	X	X
8-8	X	X	X	X	X	X	X	X	X	X
7-7		X	X	X	X	X	X	X	X	X
6-6		X	X	X	X	X	X	X	X
5-5				X	X	X	X	X
4-4	X	X	X	X	X	X	X	X	X	X
3-3	X	X	X	X	X	X	X	X	X	X
2-2	X	X	X	X	X	X	X	X	X	X
A-A	x	x	x	x	x	x	x	x	x

Wow, Double 10-18 vs 6. Makes sense, though.

And split 22,33,44,99 vs Anything. Very interesting