I played a game on GP last night and was BR1, acting last on the final hand and I have a couple of questions about what happened. Firstly was my bet more or less correct and secondly was my play correct? I will add that these numbers might not be quite right but they are close enough. As you know Max bet 500, min 10 BR2 1355 Bet 480 BR3 1305 Bet 465 BR1 1385 Bet 480 (This is me, I just matched BR2s bet as you can see) The cards came out as: BR2 T,8 BR3 10,10 BR1 6,6 Dealer 2 BR2 stood, BR3 split to T,T and T,5. My thought process was as follows - BS says to hit 12 against dealer 2, BR2 beats me if dealer hits 17 or 18 and I stand, BR3 is likely to win:lose for a push, I'm not splitting because I will no longer have the low, so I decided to hit to at least 18. As it happens I caught a 10 and bust but luckily the dealer hit 20, we all lost and I won the game. That aside how wrong was my play? What should I have done. Once again, thanks for your patience Regards Reachy
Numbers, numbers, and more numbers Reachy, I would have played the hand exactly as you did, hitting to 18 or bust trying. However, after looking closer, I think that splitting is better than that. I'm unsure whether to trust my results just yet, because I'm using an all-new process for the split calculations. Here are the results I'm getting so far, with infinite deck: Stand with (6,6): Wins 24.20% Double for full amount: Wins 38.74% Hit to 18 or higher: Wins 40.78% Split: Wins 44.52% My current calculations assume that the player uses the same strategy for both split hands, regardless of the total achieved on the first one. For that purpose, the best strategy I've found is: Don't hit a stiff, but do hit soft hands to 19 or better. tirle, arlalik, Yama, anyone else... Anyone want to confirm my results? (One more item... I approached this as a winner-take-all, when it was probably really a sit and go with prizes for first and second. Ignore that for now please.)
I must be getting the hang of this probability thing. But not quite.... Ken My figures for Standing and DD are the same as yours so I must be learning something! However I can't get the same figure for hitting to 18+. It comes out considerably lower than yours. Here's how I calculated it. I figured out what my probability of hitting totals of 18+ was including needing 2 and 3 extra cards. It came to 45.97%. Then I figured out the situations where I would win based on the different dealer totals. If the dealer busts I lose because BR3 with his split hands will win. 0% If the dealer hits 17 (13.97%) I win because me and BR2 will win and I have the high and BR3 will win:lose for a push 13.97%x45.97%=6.42% If the dealer hit 18 (13.44%) I win because me and BR2 will push as will BR3 13.44%x45.97%=6.18% Dealer 19 (13.00%) I win but only if I hit 19 -21 (an 18 would allow BR3 to beat my loss with a push) 13.00%x36.64%=4.76% Dealer 20 (12.40%) I win with the 18+ again because BR3 will lose one hand and push the other for a single bet loss so I can lose and still win. 12.40%x45.97%=5.7% Dealer 21 (11.84%) I win regardless as I have the low so can afford to lose. 11.84%x45.97%=5.44% Add all those up and you get 28.51%, nowhere near your calculation!! Where am I making the error? I haven't even begun to work out splits. I may try later if I can figure out where I'm going wrong here. Once again, you advice and expertise is greatly appreciated. Cheers Reachy Ps. I feel really indebted to you guys. Where else can somebody get coached by the best players in the world like this? Amazing!
Your mistake lies in those two lines. If the dealer makes 20 or 21, your hand doesn't matter. Correct these to: Dealer 20 (12.40%) I win regardless: 12.40% Dealer 21 (11.84%) I win regardless: 11.84% Compared to your results, that adds another 13.1%. That closes the gap between our answers to a small amount. The remaining differences come from two spots. 1) I used infinite deck throughout, while you used the 6-deck dealer outcome to start. 2) I don't know your exact calculation method for success hitting to 18+, but I used infinite deck there as well with these results. In infinite decks, starting with hard 12 and hitting to 18 or higher, the player ends up with Stiff: 0% 17: 0% 18: 11.14% 19: 11.14% 20: 11.14% 21: 11.14% Bust: 55.43%
Thanks again Ken In the words of the song "I can see clearly now..." One thing I don't quite get though is the infinite deck calculation for hitting 12 to 18+. There is no figure for busting. Is this not accounted for? Cheers Reachy
Thanks again Ken. Sorry, another question. I've been trying to figure out those infinte deck calculations and I just can't see how they've been arrived at. I even googled it so I wouldn't have to ask but I can't seem to find anything. Hope you don't mind. cheers Reachy
I use software of my own to do that, but here's the idea... It's easy to figure when you only need a single hit to accomplish your goal. Let's say you have a hard 16, and you want to hit until you have 17 or higher. That's easy in infinite decks. 17: (1/13) 18: (1/13) 19: (1/13) 20: (1/13) 21: (1/13) Bust: (8/13) If we plan to hit our hard 16 to a final total of 18 or higher, the result will look like this: 17: 0% 18: (1/13) + (1/13)*(1/13) (Chance we get a 2 on the first hit, or two aces) 19: Same (3 as first card, or Ace then 2) 20: Same 21: Same Bust: (8/13) + (1/13)*(9/13) (Chance we bust on the first card, or hit an Ace then a bust.) As you can tell, this looks like a lot of work. I'm pretty sure there's a substantial shortcut, though I haven't tried to find it since I have software that does all that. It might be useful if I were to publish a list of all the percentages for each starting hand and each desired total.
I was nearly there Thanks Ken Actually that process is how I came to my initial figure of 45.97%. It was very time consuming and the accuracy of my calculations were slightly out but I thought it was near enough. I discovered that you can use progressions to calculate the answer but I'm not sure how to incorporate them into a spreadsheet without writing long equations. Cheers Reachy
