21 (ochko)

Hi all,
I wonder if anyone have strategy/math for the game 21 (ochko, russian blackjack)? Wizard have "21 bet" at his site which have quite the same rules, but with one big exception: at 21 you draw cards yourself and not bet on different odds. As a result it looks like Double Exposure with 36 cards deck and without double/split.
Here is the game itself (I'm afraid it's not available in Demo mode) - melbet-dot-com/en/allgamesentrance/twentyone

I've never heard of it. It would be nice to play it in demo mode somewhere.

^ If you use google translate you can see the rules.

You can just change language to see rules in English :)

Sorry, I can't find free version of the game :(. It's made by 1xbet bookie (melbet is their white-label) but they do not offer demo mode. And with US blocked everywhere i can hardly give access to my account to Wizard :(. There are some videos on youtube with gameplay though if it's sufficient for you, I can give you links.

It is simply blackjack with a short deck 6-Ace, but for which

10 =10
J = 2
Q = 3
K = 4
Ace =11

where BJ pays 1:1, and AA as a starting hand is defined as 21.

Dealer must hit until 17. Player cannot double or split.

My major uncertainty: are both of the dealer's first two cards facedown??

Quote: gordonm888

Its simply blackjack with a short deck 6-Ace, where BJ pays 1:1, and AA as a starting hand is defined as 21.

Very simple to model as no hand has more than 3 cards.

I didn't understand the ranking rule, except perhaps it splits ties with the same total, until I noticed it does list their values, so the smaller cards are there - just they're J Q K! (However just using a short deck sounds an interesting idea.)

Notet: Jacks are worth 2, Queens are worth 3; Kings are worth 4; Aces are worth 11 (presumably not 1 or 11). So a deck logically has one of each 2 3 4 6 7 8 9 10 11 in each suit only, and the special case why AA counts as 21.

Quote: charliepatrick

I didn't understand the ranking rule, except perhaps it splits ties with the same total, until I noticed it does list their values, so the smaller cards are there - just they're J Q K! (However just using a short deck sounds an interesting idea.)

Notet: Jacks are worth 2, Queens are worth 3; Kings are worth 4; Aces are worth 11 (presumably not 1 or 11). So a deck logically has one of each 2 3 4 6 7 8 9 10 11 in each suit only, and the special case why AA counts as 21.

yes, sorry, I had edited my post above. Its very different than BJ.

Quote: YuraK

Hi all,
I wonder if anyone have strategy/math for the game 21 (ochko, russian blackjack)? Wizard have "21 bet" at his site which have quite the same rules, but with one big exception: at 21 you draw cards yourself and not bet on different odds. As a result it looks like Double Exposure with 36 cards deck and without double/split.
Here is the game itself (I'm afraid it's not available in Demo mode) - melbet-dot-com/en/allgamesentrance/twentyone

After rereading your above post, I assume that the dealer's first two cards are face-up!!!

Quote: gordonm888

It is simply blackjack with a short deck 6-Ace, but for which

10 =10
J = 2
Q = 3
K = 4
Ace =11

where BJ pays 1:1, and AA as a starting hand is defined as 21.

Dealer must hit until 17. Player cannot double or split.

My major uncertainty: are both of the dealer's first two cards facedown??

Yes, you are quite right. And dealer's both cards are face up.
Here is an example of the play on youtube (no links for me) /watch?v=rSS_aa_Jq7E
Just 2 buttons for the player: Hit and Stand.

I've read that 1xBet had multiplayer variant of the game named "21 online" (you play against other people, not dealer), though can't find it right now.

From "fiddling around" with MGP's BJ CA, I would guess that this game would have a better than 5.6% house edge ***

***: Very rough guess (there are at least 2 reasons I could think of for why this is a "rough guess", see below)
1 the CA counts Aces as 1 or 11, instead of only 11 , so I had to put in 4 extra 10's as a rough substitute of having 4 Aces.
2 the CA doesn't have a "double exposure" option, so I can only work out what the "rough house edge would be, if you can only see one dealer up-card".

----
"1st Draft"/Incomplete Strategy:

First, here are some of the obvious decisions (I am nearly 100% certain these are correct, also anyone could work these out by using an "educated guess"):

you should hit on:
an 11 or less vs any dealer hand
a 12 vs a dealer 4 to 11 (I don't know what to do yet for a dealer 12 to 16)
any hand less than the dealer, if the dealer has a "staying hand" / 17-21.

and here are some decisions that I am above 50% confident they are correct (but I haven't checked them):

Hit a 13 vs a 4 to 11 (possible exceptions: I am currently not sure what to do against a dealer 6, and I haven't worked out what to do on a dealer 12-16)
if you tie with the dealer on 14, then hit
If you tie with the dealer on 15 (or higher), then stand

----
Note: Other people on this site are better / more efficient at working out these sorts of things, but I thought I would make an "early" attempt.

Note 2: If you want to start working on a strategy yourself, this site may be helpful to give you an idea of how you could work out a hit/stand strategy >>> http://www.blackjackage.com/bust-out-rate.php

IMPORTANT: With "note 2" DON'T use the "Bust-Out Rate" figures on that site for the bj game in this post (instead, you need to work out those figures yourself).

Note 3: I used single - deck, BJ pays 1/1, dealer stands on 17, and ties push, for the above "1st draft" strategy

---
Spelling etc not checked

Edit: Wrong Payout - IGNORE

The rules say: If you score 21 points (or less than 21 but more than the dealer) your bet will be paid out at odds of X2.)

The English isn't very clear, but I can see two different interpretations:
- All wins are paid at 2:1, OR
- Wins are paid at 2:1, except those wins against a busted dealer hand, which pays at 1:1.

The 2nd interpretation seems weird, but might be to encourage players to hit more frequently.

I have modeled the game strategy both ways.

All Wins are paid at 2:1.

Dealer has 18 -20: Hit until your hand equals or is greater than the dealers.

vs Dealer 17: Stand on 18+, Hit a 2 card 17, Exception: St
and with a 3+ card 17 if you have fewer than 2 cards in the range 2-4.

vs Dealer 16: Stand on 12+, Hit 11 or lower

vs Dealer 15: Stand on 13+. Hit 12 or lower. Exception: Stand on 93 vs 96

vs Dealer 13, 14: Stand on 14+, Hit 13 or lower

vs Dealer 12: Stand on 13+, Hit 12 or lower
______Exceptions: Stand: 76 vs 12 (any), Stand: 13(any) vs 66, 84

vs Dealer 11: Stand on 14+, Hit 12 or lower
_____ With a 13 vs 11
vs 74 Hit any 13
vs 83 Stand any 13
vs 92 Hit: A2, T3, 94. Stand: 76

I'll post the strategy for the alternate rules interpretation in my next post.

When they speak about x2 pay they mean including your bet. So you bet 10, get back 20 (your 10 plus 10 of winnings). Payment is simple 1:1 regardless combination.

gordonm888, I wonder what payout your calculation gave you :).

Edit: WRONG PAYOUT _ IGNORE

This is for the alternate interpretation of the payout rules.

Wins against an unbusted dealer hand are paid at 2:1.

Dealer has 18 -20: Hit until your hand equals or is greater than the dealers.

vs Dealer 17: Stand on 18+, Hit a 2 card 17, Exception: Stand on a 3+ card 17 if you have fewer than 2 cards in the range 2-4

vs Dealer 16: Stand on 12+, Hit 11 or lower

vs Dealer 15: Stand on 14+. Hit 13 or lower. Exception: Stand on 13 (any) vs 87

vs Dealer 13, 14: Stand on 14+, Hit 13 or lower Exception: Stand on 76 vs 13 (any)

vs Dealer 12: Stand on 14+, Hit 13 or lower
______Exceptions: Stand: 94 vs 93 , Stand: 76 vs 12 (any)
vs Dealer 11: Stand on 14+, Hit 13 or lower

Quote: YuraK

When they speak about x2 pay they mean including your bet. So you bet 10, get back 20 (your 10 plus 10 of winnings). Payment is simple 1:1 regardless combination.

gordonm888, I wonder what payout your calculation gave you :).

Crap. Crap. Here is strategy for 1:1 payout.

Strategy Notes
All Wins are paid at 1:1.

Dealer has 17 -20: Hit until your hand equals or is greater than the dealers.

vs Dealer 16: Stand on 12+, Hit 11 or lower, Exception: Hit T2 vs T6

vs Dealer 13, 14, 15: Stand on 14+. Hit 13 or lower.

vs Dealer 12: Stand on 14+, Hit 12 or lower
______When player has 13, HIT except
Stand: 76 vs 12 (any),
Stand: 13 (any) vs 66
Stand: T3, A2 vs 84

vs Dealer 11: Stand on 15+, Hit 14 or lower

vs Dealer 10: Stand on 16+, Hit 15 or lower

I don't have a HE calculation yet, and it will be a while. Maybe Charliepatrick can provide?

TY!
BTW, I found multiplayer "21 online" 1xbet-dot-com/en/tvgames/view/twentyoneonline). Didn't tried it yet, but as I understood they take 1% from winnings. So it can profitable, having proper strategy. Of course other players do not follow "hit till 17, stand above" rule :).

Quote: gordonm888

...maybe Charliepatrick can provide?

Sorry not yet, I've only done a quick infinite deck calculation assuming an Ace is always 11 and you can continue to hit.

Dealer's	Hit	Stand
Total	on	on
4 - 6	H 13	St 14
7	H 14	St 15
8-10	H 15	St 16
11	H 14	St 15
12-15	H 12	St 13
16	H 11	St 12
17+	H if losing	else St

Quote: charliepatrick

Sorry not yet, I've only done a quick infinite deck calculation assuming an Ace is always 11 and you can continue to hit.

Dealer's	Hit	Stand
Total	on	on
4 - 6	H 13	St 14
7	H 14	St 15
8-10	H 15	St 16
11	H 14	St 15
12-15	H 12	St 13
16	H 11	St 12
17+	H if losing	else St

You ( or miplet) are probably the best to do the HE calculation quickly. No pressure though!

I did not work out a separate strategy for starting hands of 4 through 9 - the player will always hit those hands and I thought that they should then follow the "basic strategy" for their three hand total. Not sure I was correct - the multi-card hands with several small cards may play differently then a two card hand with the same total.

I found that a dealer total of 13 was really squirrelly - if you and the dealer have 2 or more cards in the range of 6-8, the answer can change a lot.

One thing that impressed me is how bad a 16 is: if you draw a card to it there are only 3 ranks with which you don't bust out: a 2,3 and 4. There's no chance of making a 21 when HITTING a 16!

Quote: gordonm888

...vs Dealer 16: Stand on 12+, Hit 11 or lower, Exception: Hit T2 vs T6...

I get that you stand on T2 vs T6 .
Assuming an Ace always counts as 11.
Stand = dealer has 11 outs (3x2 4x3 4x4) from 32 cards left in deck. EV = (21-11)/32 = 0.3215
Hit = Win 615 Tie 41 Lose 336 out of 32*31: EV = (615-336)/992 = 0.28125.

Interesting I also get you stand on 4 card 11's vs any dealer 16. That is because you bust with any of the four Aces AND you have four of dealer's helpful cards (remember dealer can't have A5!).

I'm also seeing many boundaries where the exact cards you have matter. The fun one is also 14vs11: stand 77, 662, 644 vs 92, 83, lots of 14s vs 74; 14v10 77 or 743 vs 73, 77 vs 64.

Four decks also has decisions based on the cards you have...
A simple strategy is
(i) Hit 12 if dealer shows any small card (Two, Three or Four).
(ii) Hit 12 if dealer's total is 12 or less.
(iii) Hit 13 if dealer's total is 11 or less
(iv) Hit 14 if dealer's total is 9 to 11.
(v) Hit 15 if dealer's total is 9 or 10.

Total	Hands	Decision	11	12	13	14	15
16	T6 97 88	Hit 11	H	S	S	S	S
15	96 87	Hit 11 and T2	H	2	S	S	S
15	A4	Hit 12	H	H	S	S	S
14	86 77	Hit 11 and T2	H	2	S	S	S
14	A3 T4	Hit 12	H	H	S	S	S
13	94	Some 12	H	s	S	S	S
13	A2 T3 76	Hit 12	H	H	S	S	S
12	84 66	Hit 12	H	H	S	S	S
12	T2 93	Some 13	H	H	s	S	S
11	92	Few 15	H	H	H	H	s
11	83	Hit 14 h 87 st 77	H	H	H	h	s
11	74	Some 14	H	H	H	s	S
10	82 64	Most 15	H	H	H	H	h
10	73	Most 15 st 77	H	H	H	h	h
9	72 63	Most 15	H	H	H	H	h
8	62 44	Most 14	H	H	H	h	S
7	43	Some 14	H	H	H	s	S
6	42 33	Hit 13	H	H	H	S	S
5	32	Some 13	H	H	s	S	S
4	22	Hit 13	H	H	H	S	S

Quote: charliepatrick

Four decks also has decisions based on the cards you have...
A simple strategy is

Thanks!
Do you have house edge numbers for the strategy?

Not reliably - I'm using another game (where the wizard has posted the House Edge - https://wizardofvegas.com/forum/gambling/blackjack/34686-sette-e-mezzo-strategy/4/ ) to check my logic. At the moment I agree with his strategy but not the House Edge (although I get the same trends).

I wonder if you have time to look at this 21 game again? Any idea about house edge?

Quote: charliepatrick

Not reliably - I'm using another game (where the wizard has posted the House Edge ) to check my logic. At the moment I agree with his strategy but not the House Edge (although I get the same trends).

Quote: YuraK

I wonder if you have time to look at this 21 game again? Any idea about house edge?

It really needs someone else also working on the problem so we can compare results.

In the other thread you'll see that I had had a small error in my logic but eventually got close to the figure. In other games two of us have been able to compare figures for specific scenarios to confirm or deny our logic. Also, because the strategy isn't simple, it makes any simulation harder to create (I don't do it dynamically as that's too much work).

Quote: YuraK

I wonder if you have time to look at this 21 game again? Any idea about house edge?

I used an online calculator to simulate something close to this game: it has the correct number of cards of each rank, no doubling (except on a hard 10 or 11 vs 6), no splitting pairs, BJ pays 1:1 and dealer stands on soft 17. This calculator uses the optimal strategy given these rules and the number of cards defined to be in each rank.

Besides allowing a double on 10 vs 6 and 11 vs 6 , the online calculator also insists that an Ace is 1 or 11 and that an AA is a soft 12, not 21.

Given those defects in the calculation, the house edge is 2.835%.

But, the effect of the rule A=11 would preferentially hurt the player, since he would no longer be able to hit a "soft 17" or soft "18." I have spent some time looking at that and basically I think it would add more than 1.5% to the the house edge that I calculated. So, I estimate that the house edge of this game is probably in the ballpark of 4.5%.

Not a rigorous calculation, but a fair attempt to make an estimate.

Edit: When I used the online calculator, it also allowed the player and dealer to keep drawing cards, rather than stop at 5 cards. This additional defect in the calculation probably has a negligible effect on the house edge I reported.

Quote: gordonm888

I used an online calculator to simulate something close to this game:..

Sadly I think there are a number of keys differences with this game that make using a standard BJ tool require great care.
(i) The dealer's two cards are face up, which like Double Exposure, gives an awful lot of information, especially if you normally would only know the dealer had a high card, you now have a clearer idea what they have.
(ii) The deck has been stripped of 5s Js Qs Ks (which also means standard counts don't work).
(iii) You cannot split or double (you can program this in, so not really an issue.)
(iv) Player can only take 5 cards. so sometimes will have to stand, when they might have wanted to hit.
(v) Aces are only 11. This is fair on both the player and dealer, but I suspect benefits the player as they can stand earlier and there are more dealer bust cards. The player never hits 16, so perhaps the dealer's strategy of "hitting until 17" isn't optimal for them.

I'm trying a simulation but am hitting a problem suggesting a coding bug when the player can't take any more cards. In most cases this is where the dealer has a 17-21 total and the player is forced to stand. However if I allow the player to hit 5-card hands, the House Edge goes up!

Quote: charliepatrick

Sadly I think there are a number of keys differences with this game that make using a standard BJ tool require great care.
(i) The dealer's two cards are face up, which like Double Exposure, gives an awful lot of information, especially if you normally would only know the dealer had a high card, you now have a clearer idea what they have.

(ii) The deck has been stripped of 5s Js Qs Ks (which also means standard counts don't work).
(iii) You cannot split or double (you can program this in, so not really an issue.)
(iv) Player can only take 5 cards. so sometimes will have to stand, when they might have wanted to hit.
(v) Aces are only 11. This is fair on both the player and dealer, but I suspect benefits the player as they can stand earlier and there are more dealer bust cards. The player never hits 16, so perhaps the dealer's strategy of "hitting until 17" isn't optimal for them.

I'm trying a simulation but am hitting a problem suggesting a coding bug when the player can't take any more cards. In most cases this is where the dealer has a 17-21 total and the player is forced to stand. However if I allow the player to hit 5-card hands, the House Edge goes up!

Yikes. You are right. I forgot about the dealers second card being face-up. That makes a large difference. Everything else I tried to fudge on the calculator or account for with a post correction.

This 21 game should be relatively simple to model compared to standard blackjack. No soft hands or split pairs -that is a huge simplification. And the number of possible hands is greatly reduced because there are no 5s and because the A always counts as an 11 (which chews up a lot of space.) And because there is a 5 card cap on a hand. And because dealer AA counts as a 21 rather than as a 2 or soft 12!

Of course, when dealer has a 20, the player will be hitting hard 17, 18 or 19!

I am almost tempted to model it.

Quote: YuraK

Hi all,
I wonder if anyone have strategy/math for the game 21 (ochko, russian blackjack)? Wizard have "21 bet" at...melbet-dot-com/en/allgamesentrance/twentyone

Please could you confirm whether this game is available elsewhere as I'm unable to view the melbet site for real and would like to see the game in action and double check the rules. Many thanks.

Quote: charliepatrick

Please could you confirm whether this game is available elsewhere as I'm unable to view the melbet site for real and would like to see the game in action and double check the rules. Many thanks.

Originally it's a game from 1xbet ( 1xbet-dot-com/allgamesentrance/twentyone/ ). It's also available at multiple 1xbet whitelabels. But it's not available in demo mode, as far as I can see. You can also find multiplayer version "21 Online" there.
BTW 1xbet also offers own version of sette e mezzo you discussed with Wizard in another thread, though as I can see their rules differ a little bit (can be found at the same 1xgames part of the site).

Here are rules from the game itself:

How to play
Place a bet. The initial stake is determined before the start of a game.
The maximum stake is 300000 RUB, the minimum stake is 10 RUB.
At the start of a game, the player (you) and the dealer receive two cards each. You then take one card at a time by clicking "Hit" until the total value of the hand is close to 21 (you can take up to 3 additional cards). When you think it's time to stop, click "Stand".
If you score 21 points with the first two cards (and the dealer doesn't), you win. In this case the dealer cannot take additional cards.
If the dealer scores 21 points with their first two cards (and you do not), the dealer wins. When this occurs, you cannot take additional cards.
If you score 21 points (or less than 21 but more than the dealer), your bet will be paid out at odds of x2.
If the dealer scores less than 17 points, they must take additional cards. If the dealer scores 17 or more points, they must stand.
If there is a draw ("push"), you get a refund.
If the fifth card you take contains an image of a phone – congratulations! You have won an iPhone X (and your stake will be refunded)!

If you score more than 21 points, you go bust and lose.

An exception to this rule is when you hold two Aces ("Golden Point"), which scores you 21.

Cards ranking: 6, 7, 8, 9, 10, J, Q, K, A

Value of cards according to their rank: 6, 7, 8, 9, 10, 2, 3, 4, 11

Simultaneous play on two or more tables is prohibited.

Thanks for the above, but 1xbet is not available in the UK ( https://calvinayre.com/2019/08/12/business/1xbet-shuts-uk-gambling-site-investigation/ ). Is there a site where the game is freely available?

I tried to find free games, but didn't succeed :(.
Can't you use VPN to get access to the site?

I think one needs to know that the game, in the form you describe, is generally available somewhere. One of the purposes of this site is to people advice for games that people can realistically play or, sometimes, those being developed by a designer.

You may have noticed that a different game, where there are fixed rules for drawing, is discussed here - https://wizardofvegas.com/forum/gambling/blackjack/33422-21-bet/ . The player and dealer act alternately, each having to draw a card if they haven't got to 17. It's a typical internet game where you bet on the outcome of various events and receive fixed odds (slightly less than true value).

1xbet is quite a big site. It's "language" section has like 50 flags and their casino offer >60 software providers and >12 live dealer providers (I think it's a world record for now). They were Tottanham and Liverpool sponsors afaik before getting UK licence suspension (and have contract with Barcelona now)... And i think they will finally get their UK licence back.
Games are available worldwide, but we have US ban, local European licenses, etc... So yes, it's unavailable in some countries.
I saw 21 Bet, but as you can see it's similar in basic rules, but quite different in strategy and math.

Quote: charliepatrick

I think one needs to know that the game, in the form you describe, is generally available somewhere. One of the purposes of this site is to people advice for games that people can realistically play or, sometimes, those being developed by a designer.

You may have noticed that a different game, where there are fixed rules for drawing, is discussed here The player and dealer act alternately, each having to draw a card if they haven't got to 17. It's a typical internet game where you bet on the outcome of various events and receive fixed odds (slightly less than true value).

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