ksdjdj
Joined: Oct 20, 2013
• Posts: 909
February 10th, 2019 at 11:46:04 PM permalink
Hi again,

I like to use more than one source of information (when I don't know how to work out something myself) and I am trying to work out the EV, for the hand below:

Rules: 6 decks, BJ pay 3/2, Dealer stands on all 17s, dealer peeks for BJ, split once to make two pairs, DAS.

Hand: Player 20 (T+T) vs Dealer 7
Stand EV: 0.772011
Split EV: 0.508735...*** (or is it 0.262033^^^)

***: MGP's BJ CA says it is 0.508735

^^^: Link below says it is 0.262033

https://wizardofodds.com/games/blackjack/appendix/9/6ds17r4/

The reason i would like to know this is that I am being paid by the casino \$0.31 for every \$1.00 in initial bet to split 10's vs 7, so I am either:
a) 4.67% better off to split (compared to basic strategy) after receiving the 31% of my initial bet for doing so.
or
b) 20% worse off to split (compared to basic strategy) after receiving the 31% of my initial bet for doing so.

Note: all the other "non-split" EV figures on the WoO site are the same or very close to what the MGP's BJ CA gives me.

Thanks

-------------

The link below gives me the same EV as MGP's BJ CA, so I may have misinterpreted the WoO website.

http://www.bjstrat.net/cgi-bin/cdca.cgi
Last edited by: ksdjdj on Feb 11, 2019
charliepatrick
Joined: Jun 17, 2011
• Posts: 2321
February 11th, 2019 at 2:16:46 AM permalink
If I recall the split figures assume you continue to split. A fairer way to get an estimate is to look at the various 10s (e.g. 28 37 64 55) and see the range of their hit returns (the 55 is 0.260394). Since each 10 is worth this, you'd guess about .52, but reduce it a bit as you already have two of the 10's in the deck, thus the .508735 you quote sounds feasible. If what you say is true you also think about splitting other pairs.
ksdjdj
Joined: Oct 20, 2013
• Posts: 909
February 11th, 2019 at 3:52:00 AM permalink
Thanks charliepatrick,

yes it is true, here are the other hands that you should deviate from basic strategy (see below):

pair of 10's vs A: Split and receive at least 54%*** of your initial bet (this is after dealer checks for BJ). This improves the EV by 4.3% x the initial bet.

***: this figure is 54.5% when your initial bet is in multiples of \$2.00.

pair of 10's vs 8: Split and receive 44% of your initial bet. This improves the EV by 3.8% x the initial bet.

The biggest mistake I have found in the players' favor so far, is below:

Player 6 (2 + 4 or 3 + 3) vs Dealer 10: After dealer checks for bj, they pay you at least 105%^^^ times your initial bet if you double on a hard 6. This improves the hand by at least 32.4% x the initial bet.

^^^: this figure is 105.5% when your initial bet is in multiples of \$2.00.

Note 1 : in case I haven't said it clearly before, you get to keep the "compensation" the casino pays you for basic strategy deviations, whether the hand wins, loses or draws.

Note 2: from the 20 or so best basic strategy deviations I have found so far, the game goes from a base house edge of about 0.46% to a house edge of a bit higher than 0.16%.
ksdjdj
Joined: Oct 20, 2013
• Posts: 909
August 16th, 2019 at 5:06:57 AM permalink
Hi

Sorry for the length between updates, but I now have a couple of questions and I have also done enough work on this to know that:

. The house edge for this game is ~0.46%, playing "normal" basic strategy
. The house edge can be reduced to at least*** ~ 0.046% (or ~1/2,183). when playing the "compensated" strategy.

***: I haven't seen every hand yet, but reducing the house edge by ~ 0.41% is significant.

. Another interesting point is because of the compensation received, you end up doubling a lot more when compared to playing traditional basic strategy, with this game you will double at least 36.636% of the time (when you play the correct "compo" strategy).

Q1: If i was just playing "normal" basic strategy for this game, would I be correct in saying that I would be doubling about ~9.5% of the time? (just a guess, don't know the exact figure)

Q2: Does anyone know what this would do to the variance/ standard deviation for the game? (I think it would generally increase it, but this is just a guess and i also don't have any idea of what the new figure would be)

One example of a "compensated double" that would (probably?) increase the variance, would be to "double a player BJ against a dealer 5".
With this double you are "compensated" \$1.77 for every \$2.00 of "initial bet".
So, you are giving up a "guaranteed" 150% profit (if you played normal basic strategy).
But you will be ~0.736%^^^ better off over the distance, every time you double that hand against a D5.

^^^: According to MGP's BJ CA, doubling a BJ against a 5, is worth ~62.236%, and being compensated \$1.77 for every \$2 initial bet is worth 88.5% on top of that, so the combined value of doubling on this hand is ~150.736%, less 150% for giving up BJ (pays 3/2) = a ~0.736% EV improvement on that hand.

Edit: With an initial bet of \$2 and a "compo" of \$1.77, the win-draw-loss amounts for this hand would be:
Win: +\$5.77 (x%^*^ of the time)
Draw: +\$1.77 (y%^*^ of the time)
Loss: -\$2.23 (z%^*^ of the time)

^*^: feel free to post the actual figures for these "x, y and z" %'s, since I am not very good/fast at working these out.

------
Hope this is interesting, and thanks for your time.
Last edited by: ksdjdj on Aug 16, 2019