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nick777 wrote:

I think we’re making some progress at last

Look at this example

Imagine another situation, you are playing 2 handed and have 6-6 and 7-7 against a dealer with a 10 showing, you are not the favourite under any circumstance, by splitting you lose more, you have 4 underdogs vs 1 big favourite.

The expected return is expected return per hand * bet per hand * num hand. In this case both the expected return per hand after splitting is low, and increasing num hands decreases in further. When comparing expected returns in both situation, hitting is your best option in general circumstances. Surrendering/standing is your best option using a single deck with a 7-7 vs 10 as the odds of drawing a 21 are greatly decreased with only 2 7s left in the deck.

nick777 wrote:

If you agree that this is true, what you are basically saying is that there is no advantage to playing 2 handed, so all the millions of pro blackjack players out there who play 2 handed actually have no idea what they are doing.

There are possible reasons for multi-hand play, which are listed below.

1. A reduced variance (with same overall initial bet size) — This is important, if you care about variance, as many pros do. But we aren’t talking about variance

2. A slight benefit from “depth charging” — Recall that this is counting cards in one hand and altering strategy in the second. If you are playing 4 decks with online rules (unknown shuffle, often shuffle after each hand), then the benefit will be negligible.

Why do you think just about every pro who plays multi-hand doesn’t split 10s in general circumstances (excluding a few special card-counting situations) while playing multi-hand?

nick777 wrote:

Give me an example of when it is better to play 2 handed, your odds suggest that it is never better to play 2 handed, it can only be the same as playing 1 handed, but never better, meaning, your odds of winning with any one given hand will never improve.

One situation would be playing through a large wagering requirement and wanting to minimize deviation from expected return. The reduced variance from multi-hand increases chance of falling near expected return when overall bet size is the same. However, it does not change house edge.

One possible advantage would be counting cards in a single deck. If you played 5 hands and knew the cards played in the first 4 hands, you could increase bet on the 5th and have a slight benefit. If you were playing at casino with live dealers that had known shuffle points, the benefit would be greater.

nick777 wrote:

I obviously disagree, according to your formula by playing 2 hands, the player will always lose to the house edge, only twice as much, since the bet is doubled.

How many times have I said house edge is the same when bet size and wagering are the same. If you double wagering by playing more hands simultaneously or more single-hands sequentially, then loss from house edge doubles.

nick777 wrote:

I am saying that a dealer with a 6 is one of those situations where it is better to have as many hands as possible in play, because the possibility of you winning are increased, and the possibility of you losing are decreased. Overall, not with any 1-2-3-4 hands in particular, there will be times when only 1-2-3 of your hands win and all 4 win, that is not really in question.

If you could change how many seats you were playing after seeing the dealer 6, then it would be to your advantage to sitting at all possible seats. Unfortunately you can not do this. It would not be to your advantage to split however, and reduce your expected return per hand drastically.

nick777 wrote:

By splitting your hand, the chances of the dealer drawing to 21 and beating you are 0%, technically there is no chance of it happening, even though there is, and this is going by the formula you use, so in every 100 hands you play, the dealer will still draw to 21 10 times, however, it will beat you 0 times.

The dealer has a ~10% chance of drawing a 21, regardless of whether you stand or split. He will not beat you 0 times. If he gets 21, you will almost certainly lose the several (or all) hands. REMEMBER THAT LOSSES COUNT EVEN IF YOU DON’T LOSE ALL HANDS SIMULTANEOUSLY.

nick777 wrote:

The reason is that you have an even better chance of drawing to 21 yourself, this negates the dealers 10% that beats you in the hand you are standing on, by splitting to 4 hands, you will draw to 21 around 40 times with your hands, 4 hands x 100, the dealer will still draw to 21 only 10 times out of 100, the odds actually favour my draw more to hit 21, regardless, you get the point.

Actually the dealer has a better chance of getting 21 than you do on each hand, when you split. It’s 10% for the dealer and ~1/13 for the player (only if you draw an Ace).

nick777 wrote:

I am critiquing your formula not for the sake of creating controversy, but because i find it flawed, especially in this situation, you say you will lose money by splitting to 4 hands, i say you will win 14% more money.

I also realize the fact that you have no choice but to prove yourself correct since you have a blackjack odds website that many people use, including myself on occassion, but i really think it would be in everyones best interest if you recalculated your odds for 2 handed play, it might also serve you well to have a section describing different philosophies between 1 and 2 handed play.
My odds are correct. It is ridiculous to think that odds and strategy differences change drastically for two-handed play. What happens if you are in a B&M casino and someone is sitting next to you? Do odds and strategy change drastically then to? And if he moves away, then odds and strategy return to the default?