Question about Down Under Blackjack

God, I hate to be publicly disagreeing about strategy with the Wizard of Odds! It's like playing a televised tennis match against Roger Federer.

So, meaning no disrespect, but I still think there are prima facie issues with your results.

For example, with a Medium Hole Card, a dealer 7 is a 13,14,15 or 16. "7+ Medium Hole Card" is the situation with the weakest dealer cards on the Medium Hole Card chart, yet your strategy does not reflect that. In fact, your strategy for "9 + Medium" is what I calculate for a "7 + Medium."

Going further, on the Medium Hole Card "Hard" chart, if the columns that are currently labeled 4-10 were instead labeled 2-8, I think we would be in agreement.

By the way, I agree with everything on your High Hole Card charts, except I recommend Split on A-A vs 7 and 8. I'll take a closer look at that.

I just looked at 12 vs 6 with medium hole card it's listed as hit,that doesn't seem right.Dealer total would be 12,13,14,or 15

Quote: gordonm888

By the way, I agree with everything on your High Hole Card charts, except I recommend Split on A-A vs 7 and 8. I'll take a closer look at that.

Just basing it on what I remember from exact known HC strategy, you dont split AA vs 17, 18, 19 except AA vs 17 when RSA is allowed. I don't know if the Push 22 rule changes things though either.

Quote: gordonm888

God, I hate to be publicly disagreeing about strategy with the Wizard of Odds! It's like playing a televised tennis match against Roger Federer.

So, meaning no disrespect...

As a mildly interested gambler, but very entertained spectator, I’ll just say that I’m enjoying watching from the sidelines.

Disrespect? Nah. It’s just a meeting of the minds where the problem is causing a lot of head scratching and second gussing from both parties.

Quote: gordonm888

God, I hate to be publicly disagreeing about strategy with the Wizard of Odds! It's like playing a televised tennis match against Roger Federer.

Trust me, I don't deserve such respect. This is far from the first time I've made a mistake. There are plenty of people who are on par or a little better than me at this. I just had good timing.

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So, meaning no disrespect, but I still think there are prima facie issues with your results.

Trust me, none taken.

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For example, with a Medium Hole Card, a dealer 7 is a 13,14,15 or 16. "7+ Medium Hole Card" is the situation with the weakest dealer cards on the Medium Hole Card chart, yet your strategy does not reflect that. In fact, your strategy for "9 + Medium" is what I calculate for a "7 + Medium."

Yeah, I had a bad formula. I am doing this in three separate spreadsheets and sometimes I think I'm in one but actually in another. That was the case here.

So, I updated my Medium Card strategy again. It should say 3:45 PM at the bottom.

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By the way, I agree with everything on your High Hole Card charts, except I recommend Split on A-A vs 7 and 8. I'll take a closer look at that.

Here are my numbers on that:

AA vs. 7 & High hole card
Split: 0.246153846
Hit: 0.334146847

AA vs. 8 & High hole card
Split: -0.061538462
Hit: 0.134532007

Okay, I did find an error in my algorithms for player's soft hand which changed some results on the Medium Hole Card chart. I also rechecked and changed two of the decisions on the Small Hole Card chart, namely I now calculate you should:

Hit 10 vs 8+small (not Double)
Split 2,2 vs 3+small (not Hit)

So here is my status on the strategy (I call this Version 2.2). Again, dark shaded boxes represent areas where I differ from the posted WOO strategy.



Areas of disagreement with the Wizard's latest strategy:

Small Hole Card, Hard hands: None, 100% Agreement!
Small Hole Card, Soft hands: I recommend STAND on S18 vs 6,7 and A, Wizard says HIT
Small Hole Cards, Pairs: My chart says to SPLIT on 6,6 vs 3, Wizard says HIT. I've just checked that and Wizard is correct.

Medium Hole Card, Hard hands: None, 100% Agreement! (Was a new version of Wizard's chart edited in?)
Medium Hole Card, Soft hands: S18 vs 2,3 I say STAND and Wizard says HIT
S18 vs 5 I say DOUBLE, Wizard says STAND.
Medium Hole Cards, Pairs: I say split 2-2, 3-3 and 4-4 vs 10, Wiz says to HIT those. I will check that further. Also Wizard says to SPLIT T-T vs 7, I said STAND pending an interpretation of the rules.

High Hole Card, Hard and Soft Hands: None, 100% Agreement!
High Hole Card, PAIRS: I still calculate: SPLIT A-A vs 7,8 and Wizard says HIT. Damning evidence from Double Exposure indicates Wizard is probably correct.

So, lots more agreement, now.

Quote: gordonm888

Areas of disagreement with the Wizard's latest strategy:

Small Hole Card, Soft hands: I recommend STAND on S18 vs 6,7 and A, Wizard says HIT

Soft 18 vs 6 & Small
Stand -0.19532474
Hit: -0.166058834

Soft 18 vs 6 & Small
Stand -0.221362893
Hit: -0.191135341

Soft 18 vs A & Small
Stand -0.103928497
Hit: -0.092409389

So, these are kind of close but too far apart for the number of decks to be the issue, I think. What do your numbers look like?

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Medium Hole Card, Soft hands: S18 vs 2,3 I say STAND and Wizard says HIT

Soft 18 vs 2 & Medium

Stand: -0.19532474
Hit: -0.166058834

Soft 18 vs 3 & Medium

Stand: -0.221362893
Hit: -0.191135341

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S18 vs 5 I say DOUBLE, Wizard says STAND.

Soft 18 vs 5 & Medium

Stand: 0.041361125
Hit: 0.01831607
Double: 0.036632141

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Medium Hole Cards, Pairs: I say split 2-2, 3-3 and 4-4 vs 10, Wiz says to HIT those. I will check that further.

I'll leave those alone for now.

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Also Wizard says to SPLIT T-T vs 7, I said STAND pending an interpretation of the rules.

I did some fine tuning of that, to account for a maximum of three splits, and still say to split that.

T-T vs 7 & medium

Split: 0.785422737
Stand: 0.654949056

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So, lots more agreement, now.

Again, I really appreciate your help.

Quote: Wizard

AA vs. 7 & High hole card
Split: 0.246153846
Hit: 0.334146847

AA vs. 8 & High hole card
Split: -0.061538462
Hit: 0.134532007

For: AA vs. 7 & High hole card This is a funny one, because the original posted strategy on WOO from the math report did have this as a split, which I was agreeing with!

I get:
SPLIT: 0.246153846 (Infinite deck) and 0.2604355 with the two Aces and one 7 removed from a 6 deck shoe (because there is only an 18.64% chance that the high hole card is an Ace, as opposed to 20% in infinite deck theory.)
HIT: I had an error here. My HIT S12 algorithm was botched, but since you cannot HIT any 2 starting cards and get a S12 I never worried about it. However, it bit me in the butt when evaluating this decision on a starting A-A. I have now corrected the error.

So I now get Hit: 0.334146847 (Infinite Deck) and Hit: 0.333895 (3 starting cards removed.)

So, I confirm your strategy charts on these two decisions.
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I found an error in my spreadsheet with splitting tens and a dealer high card in the hole. I forgot to cap the number of hands. After correcting that error, I show the player should always stand on 10/10 when the dealer has a High card in the hole.

Updated strategy. The time should say 8:30 PM. If it doesn't, clear out your image cache.

We are now in 100% agreement. on the entire strategy for Down Under BJ. I found an error with my algorithm for player hitting a S18 that brought me into agreement on those hands.

And yes, I agree-never split tens. For "TT vs 7 &Medium" I get Stand = 0.74089 and Split = 0.73678, even assuming that TT on a split pair will win against a dealer 22. And, to the extent that there are approximations in those values, I believe they work in the direction of STAND.

For "TT v 6 & High", I get Stand = 0.74591 and Split = 0.73884. Another close decision.

The funny thing about splitting tens is that your EV will be surprisingly low unless and until you have re-split to four hands and become eligible to have a 20 (T-T). Here are the EVs I calculate for splitting and re-splitting a "T-T vs 7+Medium" as a function of whether you wound up playing 2, 3 or 4 hands.

2 Hands = 0.45894
3 Hands = 0.68842
4 Hands = 1.2015