If mathematically considering all possible outcomes is not proof, then what is? Blackjack returns are not determined by magic and voodoo. They are determined by mathematics, and one can mathematically prove optimal strategy for a given situation.
They are saying that it is better to be a 85% favourite with 2 hands against a dealer with one hand.
Applying mathematics, win – loss and total return, and all that stuff with their numbers would prove them right, but the fact is this
Yes, all that basic algebra stuff… the kind of thing a junior high school student might see on his homework. 2*(0.85-0.15) > 4*(0.65-0.35), so 2 hands with an 85% chance of winning clearly has the higher expected return.
Are you serious?! You will lose money 0% of the time?! Think about what happens those 10% of the times that dealer draws 21. What happens if you draw a 21 in 1 hand, and <21 in the other 3? You have 1 win and 3 losses for a net loss.
This one almost made me laugh out loud. There is no mathematical formula for figuring out the probability of simultaneously losing all 4 hands?! That’s basic probablity. It seems that your probability skills are no better than your algebra skills. I don’t see why you are obsessing over simultaneous losses. LOSSES COUNT EVEN IF YOU DON’T LOSE ALL 4 HANDS AT ONCE. If you win 1 hands and lose three, you have a net loss.
We’ve gone over this many times. The dealer has a higher probability of getting 21 than you do on a given hand. The dealer has a ~10% chance of getting 21, you have a ~1/13 chance (only if you draw an ace). Remember you are drawing only 1 card, as you said you’d stand on 12 or more against a 6. Or are you taking that back and saying you’ll hit on more than 12 now?
Number of decks in play, the percentages of you drawing a card with a certain value, for example, the chances of you drawing a 8 is 16/208 = 7.69%, then compared to the dealers up card and his odds of drawing a hand.
What happens though is that the odds change while the hand is in play, and the more hands that are in play, the more complicated the math gets.
I hope you realize that people use computer simultations when the odds get too complex for hand calculations. When I say “my sim”, I am talking about a computer simulation that accounts for all of the above.
What odds formula is this? How to compute an average (hint: you have to consider losses)? How a computer simulation works?
I believe that every blackjack expert and everyone with a strong gambling mathematics background disagrees with you. Every strategy table I have ever see, and every computer simulation I have ever seen disagrees with you.
There you go again, making up whatever numbers you feel like, that number is quite obviously wrong, pretty soon you’ll be saying i will go broke with my 4 favoured hands.
You need to pay attention to what you’re saying here, you are saying my numbers are wrong, but at the same time you are admitting that yours are wrong and in contradiction with one another.
Wizard’s sim uses infinite decks. Mine uses a non-infinite number of decks. Little rule differnces like this account for the 0.02, along with not running it for an infinite number of hands.
(I hope) we’ve established it is 0.70 vs 0.56 for no resplits… the numbers I have been posting for many pages. That means each time you split 10s, it decreaeses expected return. If you include resplits, then you are no longer standing on 10s in the split hands, instead you are splitting 10s… and splitting 10s decreases exepected rertun. If you added resplits and split 10s instead of standing, then obviously overall return will decrease to below 0.56.
Think about it this way you could have had a 20 in the split hands, but instead you chose to split them again a risk getting a total far below 20. Obviously it is going to decrease expected return.
Quite a sharpie?! I wonder what it takes for someone to not be a sharpie? An elementary school student with zero algebra or probability skills?
That is certainly a convincing statement. Standing is the same strategy unanimously accepted by blackjack experts (excluding special situations), so every blackjack expert must also be wrong. Math professors, card counters, the MIT blackjack team, Stanford Wong, Wizard of Odds… all of them are wrong. That Nick is “quite a sharpie.” We must have done all of our analysises wrong, programmed all of our computer sims wrong, and have been using incorrect strategy in our playing for decades.