Last hand, Min/Max 100/500, no surrender. BR1 1200 bet 400, BR2 (me) 1101 last to act, bet 300. BR1 stand on his stiff.. me pair of 10s.. dealer up card 2. I did split and played a no bust strategy (which I think was correct) - figuring that I have less than 35% chances to lose both hands - still, I may be wrong. Would be great if we can have a chart where we can see what is the % to lose both hands after a(ny) split versus each dealer up card. (or 2 to 9 at least)
Yes, I think this may help a lot when we take the low but we have the chance to switch and take the high, giving up the low if we lose both hands after split.
Your play (and the no bust policy after it) were optimal. By splitting, you gave yourself a 76.73% chance of success vs 64.76% for both standing and hitting (either makes your hand irrelevant). I'll try to generate the split+no-bust outcome table a little later today.
Splitting Tens I had a chart for splitting (done a long time ago) but can't find the file now. From a printout for the Tens I had (can be not very accurate): D's card..+2.....+1......0.......-1.....-2 2..........44.3....3.5....19.5....9.2....23.5 3..........46.0....3.4....18.9....9.0....22.8 4..........47.9....3.2....18.2....8.7....22.0 5..........49.8....3.1....17.5....8.3....21.3 6..........51.0....3.2....18.0....7.8....19.9 7..........41.0....4.9....26.3....7.8....19.9 8..........37.7....4.7....27.7....8.0....21.8 9..........34.2....4.5....27.2....9.9....24.2 T..........31.1....4.3....22.4...17.7...25.1 A..........29.3....4.9....27.6...12.3...25.9 S. Yama
winning 2, 1, 0 bets +2 is for winning both split hands, +1 is one win and one push, 0 is for both hands push or one loses the other wins, etc. S. Yama
Complete Split Outcome Table I've posted a complete split outcome table at http://gronbog.org/results/blackjac...se both hands/split-once-no-bust-outcomes.txt These are outcomes for splitting with 8 decks 75% penetration, S17 and, the following strategy after splitting: No busting No doubling No resplitting 1 card each on split aces Basic strategy for other soft hands Also note the following strategy for when you must win two bets. It includes the proper strategy for choosing whether to double or split pairs: http://gronbog.org/results/blackjac...one/generated/complete/2.0/p1.X/strategy.html
Very nice work gronbog. Of interest in the strategy to win 2 bets is that doubling a pair of aces is better than splitting vs dealer 2-9. I have probably misplayed that hand more than a few times.
Here's Another One Thanks PlayHunter and Ken. If you hover your mouse over the cells for splitting Aces, you will see that the percentages are extremely close. Here's another one that might be of interest regarding splitting. It is my strategy for when a push is as good as a win. Note that it is recommended to split almost all pairs (exceptions: all 5,5, all T,T and 9,9 vs 7 and 8). It turns out that splitting can be an effective way to manufacture a push. Note also that we hit all 12's, hit 13 as if it were 12, stand on A,6 vs 7 and A,7 vs A.
Could this be the latest ever (genuine) reply to a post? (I found my way to this ancient thread via some keyword searching, looking for information on split probabilities.) - Firstly, Gronbog, it looks like there is a link missing from your final post. Am I right in thinking it is this one? - https://gronbog.org/results/blackja...one/generated/complete/0.0/p1.X/strategy.html (I did some hunting inside your directory structure; hope you don't mind!) Secondly, is the post-split strategy the same no-bust strategy you gave earlier? Wouldn't the best strategy for 'push is as good as a win' involve playing the first hand more aggressively than even basic strategy, always hitting up to a non-stiff total (or busting in the attempt). The second hand would then be hit to at least the same total as the first (and if the first was a bust, then the second reverts to a 'push is as bad as a loss' strategy). My logic is that the higher of the two hand totals needs to beat the dealer (or they can be the same and both push), therefore standing stiff on the first hand serves no purpose - it would just mean the result is dependent on the second hand beating the dealer or on the dealer busting. So you may as well try and improve the first hand, and if this is successful then the second hand only comes into play if the dealer beats or pushes with the first, therefore hit it to the same total.
I'm happy that you were finally able to make your post! Yes, you found the correct strategy. I recently wrote more about it here: https://www.blackjacktournaments.com/threads/free-money-in-michigan.9179/page-3#post-54052 I had not considered hitting the first hand of a split to 17 or higher. My initial thought is that standing on a stiff still gives you the opportunity to hit your second hand to 17 or more. However successfully hitting your stiff first hand to a non-stiff total then gives you the opportunity to hit your second hand even more aggressively. So it would appear that your suggestion does have value.
So you did! Apologies, I missed that, despite posting in that thread. Do you happen to have a table of outcome probabilities for this strategy, like the one you posted for no-bust? I too am chasing streaks, making it doubly ironic that I missed/forgot the earlier discussion. There's an additional twist, though, which may warrant a PM, rather than broadcast it to the world. Thanks. I think the optimal strategy is quite a complicated question. E.g., It seems to me like it may even make sense to hit, say, a 17 vs 10 (and maybe other dealer up cards) on the first hand, there being no value in pushing unless the other hand also turns out to be a 17.
I could generate one but it might not be soon. I would have to configure the strategy as described and then run a simulation. Not all that difficult but I'm deep down the rabbit hole on another project at the moment and will be for the foreseeable future. I used to have the table for playing the first hand of the first split, but I can't seem to find it. That I could easily regenerate in the background while I work on other things.
Don't worry; it's not vital. I just thought it might have been something that got recorded along with the strategy table. In actual fact, the success rate figures that show when you hover the mouse probably provide the most useful information. I was just curious about how those figures break down into 0 and +1. Anything you can easily provide would be useful. I'm a bit confused, though. I thought you were saying that this particular idea of aggressively playing the first hand to set the base for the play of the second hand was not something you had looked at?
If the initial split strategy supports it then it would be more accurate to say that it's something I had forgotten about. I came up with the strategy in the other thread from scratch based on logic alone.
I see (I think). So would the overall strategy being determined be the following? - "Hit the first hand to whatever total minimizes the probability of an overall loss, given that the strategy for the second hand will be - Hit to a total greater than or equal to the first hand's."
On reflection, I think I have been overlooking the cost involved in hitting and busting the first hand - You are then constrained in how you can play the second. So I guess even standing on a stiff can have more benefit than risking a bust (if it means a sufficiently greater chance of making 18+ on the second hand.)
The regeneration of the strategy table for the first hand of the initial split is partially complete. I can tell you that, at this early stage, it does recommend hitting all the way to 17 against most dealer up cards. It also recommends hitting some 17s. I'll wait for the software to declare the strategy converged (I'm doing this by simulation) before posting the strategy and commenting further.
I've regenerated the strategy for "push is as good as a win", or "the streak chasing strategy", however you want to look at it. I've placed the new initial hand strategy at the same link as before: https://gronbog.org/results/blackja...one/generated/complete/0.0/p1.X/strategy.html This version assumes that you will not resplit but it turns out that the strategy is the same and the expected success rate (52.73%) is virtually the same as for the previous "split to 4 hands" assumption. In other words, the ability to resplit is definitely not worth the complication, so our intuition to ignore it was correct. As for the strategy for the first hand of the initial split, I remember now why I couldn't find "the" strategy. It's because the strategy depends on the potential strength of your second hand (i.e. which rank you split). The good news is that there are only 3 strategies and that they are so similar that you can think of them as modifications of each other: If you split 2s, 3s, 4s, 5s or 6s (you actually should not have split your 5s but the strategy applies anyway): https://gronbog.org/results/blackja...ne/generated/complete/0.0/p1.X2/strategy.html The main rules are to hit to 17 vs 2-7 and hit to 18 vs 8-A for hard hands and to hit to A,8 except A,7 vs 6 and 7 for soft hands. If you split 7s, then there is only one difference in that you hit A,7 vs 6 https://gronbog.org/results/blackja...ne/generated/complete/0.0/p1.X7/strategy.html If you split 8s, 9s or Ts (you should not have split your T,T, however ...) then you hit to hard 18 except vs 7 where you stand on 17. https://gronbog.org/results/blackja...ne/generated/complete/0.0/p1.X8/strategy.html So it looks like Colin's intuition on playing the first hand of a split was correct.
