callipygian said:
There actually is a problem with the split charts which I'll go into later, but there's an additional problem with your analysis here. The first set of charts was for the hands to be split - that is, for 2,2 vs. 2, you should win a certain percentage of the time. The second set of charts is for the hands after they're split - that is, a single card 2 vs. 2. Because splitting 2,2 vs. 2 involves additional decision-making, I thought I'd be giving you something closer to what you wanted by giving the raw percentages.
If you calculate P(1)*Soft(13)+P(2)*Split(2)+P(3)*Hard(5)+P(4)*Hard(6) ... +P(10)*Hard(12), you should get 42%. (In this case Split(2) = 52%)
Think I still might be confused. I'm not sure I'm following what the difference is, chart-wise, between "to split a pair of 2's" and "actually drawing to the split 2's". I just assume that if you decide to split them, you're automatically making the decision to draw, at least one, card to each hand. Like when you see an EV table in books, sites etc, aren't the splitting tables assuming that your EV is such and such IF you, in fact, play out the split hands (draw to them according to best strategy). I assumed your first split chart was assuming the split 2's were played out fully and that your odds are, on average, that you'll win 42 times out of a 100 if you do in fact play them out as "correctly" as you can. But actually the second split chart is what reflects that, not the first?
No, this is an oversight on my part. I shouldn't have posted the split charts, as they contain a small probability that a single card 2 gets dealt a 7,8,9 and then doubled. The doubling is mixed in with the win percentages so all the split charts are going to be off.
That's cool. No problem. I still appreciate all the charts. I just wanted to make sure I wasn't going crazy trying to figure why they weren't adding up to 100%...lol
You'd look up doubling hard 4 to see what the win percentage is doubled, standing hard 4 to see what the win percentage is standing, hit hard 4 to see what win percentage is hitting, and split 2 to see what win percentage is splitting (except that the split charts are wrong).
But the problem is I don't see totals of 4 anywhere on the chart (with the exception of the split charts). All of them, when I scroll the arrow over all the way to the far right sides of the table all start at a minimum player's hand total of 5.
No, and this is why people usually calculate EV. Doubling means you get one card only, whereas hitting allows for more decision making. It's quite possible - and is true for a lot of soft doubling - that your win percentage actually DROPS as a result of doubling.
For example, let's say you have a coin flip which you win 80% of the time and lose 20% of the time. Would you rather play that game, or a coin flip which you'll only win 70% of the time, but for double the stakes?
EV for first game = 0.80*(+1)+0.20*(-1) = +0.60
EV for second game = 0.70*(+2)+0.30*(-2) = +0.80
You're right. That was my mistake. See, and I even warned myself in previous posts that I knew that doubling vs hitting situations are the one "slippery slope" with just using a "winning the hand odds" chart!
So I was aware of this. I simply wasn't thinking. I forgot that when doubling, ONLY one card can be drawn. This obviously makes all the difference in the world compared to hitting. I think I was messing up the actions of splitting and doubling in my mind. With splitting (except aces) you can still endlessly draw (until you bust anyways). I was incorrectly thinking of that when I was thinking of doubling vs hitting being the same...
Win percentages aren't the end-all, they're a stepping stone on the way to calculating EV.
I'm sure that's true but, like I said, for whatever reason, just straightforward "how many times can I expect to win this hand out of a 100" percentages seem to register with me better in more "practical", relatable terms (again, provided such above exceptions AREN'T skewing the percentages in a misleading fashion). But this is because I already know basic strategy (largely). It's true that if someone didn't already have a chart memorized, they'd be better off to first look at an EV chart than just a winning the hands chart or they might come across some hands where they'd get the wrong idea. But if you already know WHAT to do with a hand then EV tables just kinda seem confusing to me. At that point, after knowing WHAT to do, then I just enjoy knowing more of the general probabilities of that "what to do" - in other words, just how often will I win this hand now that I know "what to do". It just seems more basic, relatable and even curious, in a trivial way. It doesn't mean I try to memorize all these winning the hand odds but I'm just one who's always been fascinated with just the general probabilities, frequencies of the game. In that sense, such things are more interesting, straightforward to me than all the decimal rich integers mixed together on EV charts (even if the EV charts are more "important" to know).
For instance, I don't necessarily need to know (nor can I relate in practical everyday math terms) that such and such a hand has a -11% expectation to stand rather than a -9% if you hit it. This just simply tells me its a little better to hit. That's critical and helpful yes. But, in everyday math terms, I can "envision" it better if I just knew that such and such a hand I'm only likely to win 38% of the time if I stand or 44% if I hit. Now THAT I can relate to better (in general math terms). I don't have to "imagine" what precisely a -11% expectation really means (in money terms) or how much worse is that really compared to the -9 expectation (in money terms). But seeing things in a "black and white" 38% or 44% is easier to everyday sense. I know, without even thinking, what something 44% means, odds-wise. It just means what it looks like - I should win about half the time but isnt quite a winning situation, regardless which one I do. I still know the hitting percentage is the "correct" one to play. Of course it isn't difficult, necessarily, to get this same idea from using the EV tables BUT it doesn't hit the mind in as straight-forward and relatable a way. You have to kinda just "guess" that a -9% expectation isn't TOO bad, it's probably about, oh.... maybe 40 times out of a 100 I'll win this hand here??? And in the minimum of cases where just a "winning the hands odd" chart would lie to you (doubling vs hitting or surrender), I'd think one could easily color code or note that in this particular percentage, don't pay attention to it, just do this instead...). In effect, such a winning the hand chart could STILL be an EV chart (if these corrections/color codes were added). **Note: I used the 38% and 44% in relation to the -9 and -11 EV numbers as pure random illustration purposes. I actually have no idea if 38% and 44% translate from the EV numbers I made up. That's the whole problem!!! lol. But at any rate, this is just all my opinion and babbling. I'm sure most people don't have any problem at all with EV charts, or maybe just don't like/care what winning the hand percentages are, even just for trivial purposes. It probably just comes back to me and my poor math mind again...
