Single Deck Blackjack

Does anyone have a link, or would be kind enough to share a single deck Blackjack (Microgaming rules) players expected return chart at all?

Rules:
Single Deck
Dealer Stands on Soft 17
Dealer does not peek for BJ. All bets lost for dealer BJ
No double after split
Only split once
No surrender
Player may draw to split aces

What I am looking for is something like on the Wizard of Odds site under /games/blackjack/appendix/5/) however, the rules based in that chart do not reflect the specifics of the game I am looking for.

I play a lot of single-deck to those rules and would like to be able to asses how 'fair' my results are.

Many thanks in advance!

Hi nbond, and welcome to the forums. The wizard has many utilities for a lot of games. One of which happens to be a blackjack house edge calculator. It can be found here: https://wizardofodds.com/games/blackjack/calculator/

With the rules you've given, assuming the game is 3:2 for blackjack, I'm showing a House Edge of about .10%. A really good game rule wise, but the penetration and the heat would be what I'd worry most about if you're looking to count at this game. Also, if it's online, lol. =)

Next, if you're looking for a specific card to card and hand breakdown of expected return very similar to Appendix 5, I'd imagine that would take someone a bit more work to produce. Also, while the percentages are in no way 'exact'... "most" of those percentages won't change that much from Appendix 5 (some will due to the DAS, etc, but not a mountain of a change all the same). Perhaps PM to the Wizard requesting said information, as I'm not sure how he programmed it and it may or may not be easy for him to change rules and provide an additional result with your rule set.

Thank you for the quick reply Romes.

I have seen the edge calculator, I thought about using an overall percentage to work out fairness of my results, but unfortunately due to fluctuations in staking, I do not believe I could make this work accurately, for example, playing £100,000 worth of single deck, may show a profit (thus above expectation) but this could be down to pure luck in staking alterations between times of playing. If that makes sense!

What I want to do is assess each time I play, and I can record each particular game through automation, and then establish whether or not after each session, how fair were the results. Obviously the aim would be to combine with multiple sessions to garner the greater picture, regardless of P&L.

E.G, I was dealt XX. Dealer has X. Therefore upon expectation of perfect strategy play from this point, I should win Y%.

The link I tried to post (but I am not allowed) is the wizardofodds URL, followed by /games/blackjack/appendix/5

How do i message the Wizard himself?

TIA

Ah, so an online single deck game that you want to check the fairness of. Either way you're going to have to play a lot of hands to get statistically relevent data, so you could use the overall house edge in your EV calculations... Compare to 2SD and 3SD after X hands (something like 50k) and you should have real good picture of what's going on. If it's a $10 min bet,

OriginalSD = 1.15*10 = 11.5

EV(50k hands) = (10*50,000)*(-.001) = -$500
SD(50k hands) = Sqrt(50,000) * 11.5 = $2571.48... 2SD = $5,142.97... 3SD = $7,714.44

So you could still be up ~$7200 after 50k hands due to natural variance. In order to prove you're down (since it's such a low HE game) you're going to have to play a lot more hands.

EV(200k hands) = (10*200,000)*(-.001) = -$2,000
SD(200k hands) = Sqrt(200,000) * 11.5 = $5,142.96.... 2SD = $10,285.91... 3SD = $15,428.88

While it's true you would get your answers quicker via exact hand comparisons and expected returns, you'd still have to blast through hundreds of thousands of hands either way... This isn't something I'd recommend checking on, as you surely could put that amount of hours in to something more productive in either gambling/AP or even with your life. I'd just put out a thread with your individual results to the named site and say while you don't have proof you feel the game is not the return they show. Then move on with your life to the next thing.

You can PM anyone by clicking their name in a thread and clicking "New Message" on their profile.

Thank you Romes once more.

Yes, it is more about assessing the fairness of the results over a long period of time. Playing 100s of thousands of hands is not a problem in terms of time or productivity for me, nor is expediting the automation of recording each hand and then therefore recording the data. I just need the expected return per hand, ideally.

I am interested to hear your take on using the SD, i suppose as a basic approach this could work. Although, as mentioned I would like more accuracy, because stakes can vary from anywhere around the £40quid to the £200 mark. Again, a significant range. Would you say this would affect the results significantly the way you calculate it above?

Thanks

Definitely would effect the outcomes. Essentially before I was assuming a flat average bet. If you're ramping your bet you'd need to come up with an "average" bet. If you're counting then your bet at the specific True Counts will come with frequencies. Thus you can find your average bet per bet at True Counts. If you're not counting, you'll just have to estimate your average bet best you can... but a change in average bet will change OriginalSD, which will change all of your EV and all of your SD's. Yes, using the SD approach is a bit basic, and if you wanted a further level of detail I'd recommend crunching the numbers with an application or simulation. Curious though, why would you bet more at any given point on a game you feel is not fair? ...especially if you're not counting? Are you depth charging? All the same though, if you think the game is not fair the best way to show is to flat bet to keep consistency in your numbers and pay a massive amount of hands and then decode the statistics.

I'll still say again, I don't think this is worth the negative EV to find out. Hell ,with an average flat bet I showed above you could be within 3SD and still be down $20k... Thus you could lose $20k and not have proven anything. There's a lot more you can do with your time and money!

This reminds me of this article, I recommend you take a read just to get an example.
https://wizardofodds.com/online-gambling/casino-bar/
Romes is totally right, and you can't really prove anything based on just your "results" unless you play billions of hands. You might show a huge loss and it can be explained by variance, it's not worth it. But from the study I assume you can gauge whether a game is fair or not without playing that much, by looking at specific occurrences. It is beyond my statistical expertise and I believe it would take some effort.
If you want to do that, all the power to you!

I think it would be easier to record each card dealt and in which order. Then you could do some fairly simple analysis to see if you are getting a reasonably random sampling of cards or if certain hand compositions or hit cards are coming up more often than they should. This would give you results even if you change your stakes or even play games with different rules, therefore a different house edge.

Thank you all again for your replies.

I suppose recording individually and taking 'snap' samples could work over a long time to see how we get on (looking at the methods of the Wizard on that link r.e the Casino Bar Blackjack,

I think the blackjack hand calculator on the site can give me what I need for now - if I set the parameters to the specific game it does tell me what the probabilities are per hand each time.

I appreciate all your guys time and ideas on this subject

Utilising the calculator on the Wizard site for my game, I am looking at how the probability of the following is created (if anyone can tell me)

In a hand where a split is the optimum play, I have an expectation. Let us say I pull A,A vs Dealer 10 and I split them.

According to the calculator the Expectation is +0.104690.

However, what facets is this probability derived from? Especially, let us say in the situation, whereby I win one hand and lose on the other, meaning net position is no gain or no loss. If recording the outcomes this way in attempt to find fair results, would you write this as 1 win and 1 loss? Or as 1 push?

Similarly, if you won one hand and pushed another. Again, net position is a gain, but not by the expected amount (because you are expected to win both hands), so would you record as 1 win and 1 push? But the win is not a full win, if you get my jist.

Am i trying to establish how the Expectation of +0.104690 covers this possibilities....

Many thanks in advance

You have to calculate all possible outcomes over a large sample size. Not all three scenarios you mentioned are equally likely to happen either.

Quote: nbond89

Utilising the calculator on the Wizard site for my game, I am looking at how the probability of the following is created (if anyone can tell me)

In a hand where a split is the optimum play, I have an expectation. Let us say I pull A,A vs Dealer 10 and I split them.

According to the calculator the Expectation is +0.104690.

However, what facets is this probability derived from? Especially, let us say in the situation, whereby I win one hand and lose on the other, meaning net position is no gain or no loss. If recording the outcomes this way in attempt to find fair results, would you write this as 1 win and 1 loss? Or as 1 push?

Similarly, if you won one hand and pushed another. Again, net position is a gain, but not by the expected amount (because you are expected to win both hands), so would you record as 1 win and 1 push? But the win is not a full win, if you get my jist.

Am i trying to establish how the Expectation of +0.104690 covers this possibilities....

Many thanks in advance

A split has 5 outcomes:
+2 +1 0 -1 -2
i.e. win both hands, win 1 push 1, push both or win 1 lose 1 ...etc. The +0.104690 is derived from doing billions of hands. Each hand has as an outcome one of those 5 numbers and taking the average.
PS: This is how to get the expectation for a given play (hit-stand-double ..etc). The expectation the calculator gives you for a split is assuming you play basic strategy after you split. If you want to figure out what the best play is (derive basic strategy) you do the above for every possible decision and pick the one with highest expectation.
Edit: Previous statement was for splitting aces, standard split has 17 possible outcomes (assuming maximum splitting of 4 hands)
+8 +7 ... 0 .... -7 -8
The +8 -8 are if you resplit to 4 hands and double all, win or lose all. The rest is the same, average all results.