Hello all Made a cock-up of my final hand on a mano a mano game at blackjack21.com last night (You saw me do it fgk42!). I’ve performed my own analysis of the play and confirmed that it was wrong and thought it’d make an interesting teaser. I always find these situations difficult for some reason – you are BR1 acting first, BR2 is just less than a max bet behind, and you get bad cards, BR2 gets good ones. Arghhh! Actually when I say I’ve confirmed the play was wrong of course I’m not totally sure of my working out so I’ll let people have stab at it, post my own calculations and hopefully the more knowledgeable players will confirm my/our results either way As I’m typing this I’ve just realised that it’s a 2 deck game at bj21 when you play mano a mano so my calculations are inaccurate!!! However for the sake of the teaser let’s pretend it’s a 6 deck game and take it from there. (Interested to see what the best play is with 2 deck calculations but haven’t got time at the moment to do them) Last hand, max bet $1000 min $100, surrender allowed. Me, BR1 to act first. BR1 – BR $3000, bet $1000 BR2 - BR $2091, bet $1000 Before you say anything I know my bet was wrong!!! I think I should have bet somewhere between $600 and $900. Cards were: BR1 – K, 5 - 15 BR2 – 8, J – 18 Dealer - 2. {Edited this bit because I forgot it. The dealer actually had an Ace but for some reason I did my calculations for a dealer 2! I'm losing it } So what’s the best play? I hit, which I felt was wrong as I was clicking the hit button, pulled a 7 and bust. BR2 stood and the dealer pushed him. I looked at 5 strategies – Standing, Hitting once, Hitting until I got to 18 or bust, Doubling or Surrendering. I tested them in 2 scenarios; the 1st being with my original bet, the 2nd being with a bet of $900. If anything it demonstrates to me how much of an affect a bad bet can have on the chances of a positive outcome. Cheers Reachy
nothing wrong with that! Hey Reachy, What are you talking about. I thought the outcome was marvelous Actually I was surprised at the max bet myself. You forgot to mention that the dealer had an [2 is the correct card no 8 as originally posted] Given the bet, your hand, etc.. The only thing I can think of was if you surrendered. Had you done that I would have stayed and pushed. You 2500 Me 2091 What I would be interested in is what the "PROPER" bet by BR1 would have been in this case. Looking forward to seeing people's answers
I thought the dealer had a 2 showing... but infact it was an Ace. That has completely cocked all my calculations up!!! In the words of Homer Simpson "D'oh!!!" Reachy
Done calcualtions for Dealer Ace.... Assuming (and it's a big assume!) that my calculations are right things are different now that the Ace is the dealer up card (surprise, surprise!) but not exactly in the way I thought. Lets put it this way I feel slightly better about my play but not about my bet! Can you tell me now what the best play is for both my actual bet and the "better bet" (cos there always is one!) Cheers and sorry if I've confused anyone (including myself). Cheers Reachy
This is what I think... could be wrong though! Well here are my answers. Comments from the more mathematically minded appreciated First, an admission. I have made a complete cock-up of this post. I posted the original teaser with a dealer 2 and then thought that I’d got that wrong and changed it to dealer Ace. I now realise I was right the first time!!! Still it’s made for interesting problem solving and if I’ve got my answers right I still feel I’ve learnt something. The scenario: Last hand. Bet spread 100-1000. Surrender available BR1 – 3000, Bet 1000, Acts First BR2 – 2090, Bet 1000 Cards BR1 – T,5 BR2 – T,8 Dealer – Ace (My calculations for 2 will come later!) Q: Best play with actual bet vs. better bet (900). I’m sure there is a better bet than 900 but that’s what I would have gone for. 550 would have done the job also. The biggest influencing factor in this hand was the bad bet I placed at the start. As you will see from my figures all the playing decisions were pretty much similar but the better bet sees my chances increase significantly. “Bad” Bet Standing – 62.27% Hitting Once only – 64.89% Hitting to 18+ or bust trying – 64.99% Surrendering – 64.49% Doubling – 33.34% Apart form DD any of the other plays would do but hitting to 18+ or busting is slightly ahead. “Better” bet Standing – 81.19% Hitting Once only – 77.99% Hitting to 18+ or bust trying – 77.16% Surrendering – 64.49% Doubling – 33.34% Again they are all pretty close but Standing is now the best bet. The most significant thing is that my chances now go from 65% to 81.2%. That’s an over 16% improvement. Shows what difference a bad bet can make. Same again but with Dealer 2 this time “Bad” Bet Standing – 72.59% Hitting Once only – 61.99% Hitting to 18+ or bust trying – 59.63% Surrendering – 50.68% Doubling – 36.21% “Better” bet Standing – 86.03% Hitting Once only – 71.29% Hitting to 18+ or bust trying – 68.28% Surrendering – 50.68% Doubling – 36.21% As before it’s the bet that has the biggest influence on the outcome of this hand. I’d be unlucky to lose any of these plays (except DD of course) but with the better bet it’s almost locked up. So what do you think? Can anybody verify my results? Can you be bothered ? (Don’t blame you if you don’t) Would be nice to know I’m on the right track though. Cheers Reachy
Extra, extra.... Addendum: I’ve realised that in each scenario if you (BR1) hit and get 18 or higher the right play for BR2 is to hit/DD. This could affect things significantly and possibly change what the correct play for BR1 is. The impact will be to reduce the chances of either of the hitting strategies being successful and I suspect that in the "Dealer Ace, bad bet" scenario standing will now become the optimum strategy. I would calculate it but I've spent enough time on this already today! My boss would kill me if I had one. Cheers Reachy I’ll shut up now!
Thoughts on Teaser Using the numbers in Stanford Wong's book on CTS on page 131 where he gives probabilities for 2 players against the dealer one can construct a chart as follows: LL means A & B both lose. LP means A loses and B pushes. The 1st letter of the paired letters is A's result against the dealer; the 2nd letter is B's result against the dealer. If we add all the probabilities where A is under the paired letters then we see the probability of A leading after the hand. The last 4 paired letters are always for player A provided A has the larger bankroll. ..............................LL...WW...LW...LP...PW.......PP..WL..PL..WP (A) 3000...1000.........A.....A......B.....B.....B.........A....A....A...A......=>81% (B) 2090...1000 ..............................LL...WW...LW...LP...PW.......PP..WL..PL..WP (A) 3000....900..........A....A......B.....A.....B.........A....A....A...A......=>86% (B) 2090...1000 Note with a 900 bet A now leads when he loses to the dealer and B pushes. This LP occurs 5% of the time according to Wong's table of probabilities. Of course that assumes the hands are paid off at the initial bet. It does not take into account BJ premiums or Double or Split wins or loses. It also does not into account all the crazy plays players make on the last hand. However the tables are still very useful. As a side note a bet of 100 by A would work as well but if B gets a BJ or double down no amount of doubling by A will enable A to catch up. My results are shown below for when after the cards are delt. H17 would mean hit to a hard total of hard 17 or more and then stand. H15 means to stand with the inital cards. Player B always stands with his hard 18 for the results shown. Dealer stands on soft 17. (A)...3000...1000.....10+5......Action? (B)...2090...1000.....10+8......Stand Dealer......................A ...........................BlueLight.......................Reachy A's Action........6 Deck.......inf deck...............? Deck .....H15...........61.94%......62.21%...............62.27% .....H16...........64.80%......64.87%...............64.89% .....H17...........64.91%......64.98%...............------ .....H18...........64.93%......64.99%...............64.99% .....H19...........61.12%......61.25%...............------ .....SUR...........64.43%......64.46%...............64.49% .....DBL...........27.27%......27.18%...............33.34% ?? (A)...3000....900......10+5......Action? (B)...2090...1000......10+8......Stand Dealer........................A ............................BlueLight.....................Reachy A's Action........6 Deck.......inf deck..............? Deck .....H15...........81.03%......81.11%...............81.19% .....H16...........77.98%......77.95%...............77.99% .....H17...........77.65%......77.61%...............------ .....H18...........77.18%......77.14%...............77.16% .....H19...........74.70%......74.70%...............------ .....SUR...........64.43%......64.46%...............64.49% .....DBL............64.80%......64.87%...............33.34% ???? (A)...3000...1000........10+5......Action? (B)...2090...1000........10+8......Stand Dealer..........................2 .............................BlueLight.....................Reachy A's Action........6 Deck.......inf deck..............? Deck .....H15...........72.55%......72.53%...............72.59% .....H16...........62.09%......61.94%...............61.99% .....H17...........61.05%......60.92%...............----- .....H18...........59.76%......59.59%...............59.63% .....H19...........55.39%......55.28%...............----- .....SUR...........50.81%......50.66%...............50.68% .....DBL...........30.65%.......30.58%...............36.21% (A)...3000....900.........10+5......Action? (B)...2090...1000.........10+8......Stand ..............................BlueLight.....................Reachy A's Action........6 Deck........inf deck...............? Deck .....H15...........86.07%.......86.02%................86.03% .....H16...........71.43%.......71.28%................71.29% .....H17...........70.06%.......69.94%................------ .....H18...........68.43%.......68.27%................68.28% .....H19...........65.00%.......64.88%................------ .....SUR...........50.81%.......50.66%................50.68% .....DBL...........62.09%.......61.94%................36.21% We differ significantly on the double option for player A. I tried inputting an initial bet of 1800 for A and setting the hard standing to 16 in a few places; this is the same as doubling 900. I got the same result but with all the work I can only hope there is no error. I also checked different actions for B after A finishes playing his hand and found no appreciable gain for B; but I did no lenghty tries. BlueLight
Thanks Bluelight I like the analysis using Wongs tables. What's interesting is that with the bad bet scenario after the cards have been dealt the odds decrease from 81% to 64.99% but with the better bet they only drop from 85% to 81.19%. BR1 already has the weaker hand but combine it with a weak bet and the chance of winning decrease significantly. In fact the bad bet has just over 4X the negative impact on overall odds compared to the good bet (decrease of 16.01% vs 3.81%) As for the dicrepancy in the DD calculations unfortunately I have deleted the excel file with them on so I don't have them to hand. I'll look into them again as I would like to see where the differences lie. I'm here to learn!!! Cheers Reachy
Thanks Bluelight, Thank you for the time and effort you put into that post. I am very thankful for that. It helps me a lot to be able to understand and hopefully contribute to my learning curve. Thanks again PS Thanks to U 2 my British friend [for the post and the game :laugh: ]
