Cutting the house advantage to 0.7868% - guaranteed without even Basic Strategy

#1
I don't know if I should be saying this, but I just can't seem to see the flaw in how I've figured this out.

Okay, I read online (and it makes sense to me) that the source of the house advantage in Blackjack is the situation of double busting. If both you and the dealer play the same strategy, the house advantage comes from the fact that when you and the dealer bust (or would have both busted), the house gets the chips. If playing the dealer's strategy busts 28% of the time, then the starting house advantage without any strategy is 0.28 * 0.28 (when both you and the dealer bust) = 7.84% house advantage.

It is only because of player options like doubling down and splitting, that people have managed to reduce that number. However, I looked at that calculation (did a little subsequent empirical testing at home) and believe I have figured out a way to reduce the starting house advantage - before player options - to 0.7868...%

Answer: play in a team of four. Why?

Because then, the house advantage looks like this. If all of you bet the same amounts, and use the same strategy as the dealer (or at least as optimal statistically), then the house gains the advantage ONLY when 3 of you bust, or all 4 of you bust. This is because if the dealer busts and 1 or 2 of you bust, the other 2 or 3 people will win - and essentially cancel out the losses of players who busted. It becomes a team vs dealer TIE (or slight win).

So, back to our old calculation. The house advantage now comes when the dealer and 3 people bust, and when the dealer and 4 people bust.


0.28*0.28*0.28*0.28 = 0.00614656% (the chance that the dealer and 3 people bust)

0.28*0.28*0.28*0.28*0.28 = 0.0017210368% (the chance that everyone busts)

0.00614656% + 0.0017210368% = a total house advantage of 0.7868% (rounded)


So, now I'm here with my numbers and my hypothesis, looking for some discussion. The scientific method would be proud. I just hope that if I'm right, casinos don't change the game of Blackjack forever after seeing this =S.
 
#3
then I guess I'm wrong? But where - can someone please explain :confused:

-------------------------
EDIT:

I think I've found one area where I'm wrong.

The chance that 3/4 people will bust with the dealer is not 0.28^4. That is the chance that one combination of those people will bust.

The number of combinations of 3 people, with 4 people at a table, is 4. So now we're up to:

0.28^4 * 4 = 2.458% chance of busting
+0.0017210368% (everyone busting) = 2.63%

but that's still better than the base percentage of 7.868%, right?!
 
#4
I don't think your math is correct.

Even if it was, what would it say? What has busting got to do with win percentages? If you don't bust, it doesn't mean you win.

Also, are you aware of what the house edges are with basic strategy? They are smaller than what you are talking about.

I guess im trying to understand what you are trying to say here...
 
#5
Even if it was, what would it say? What has busting got to do with win percentages? If you don't bust, it doesn't mean you win
Well, the reason why blackjack is 'hard' to make money with, is because the house has a statistical advantage over the player.

The statistical advantage in blackjack comes from the fact (i believe) that in situations where the dealer busts AND you bust, the dealer still 'wins' in the sense that the house gets your chips.

The strategy here is to decrease the amount that you bust. By turning your one hand into four hands, statistically it lowers the chance that more than half your hands bust when the dealer busts. In calculating these probabilities, we only care about the situations where both the dealer and the player bust, because in all other situations the player and the dealer have an equal chance (there is no house advantage involved. Chances to win are 50/50, if you don't include the player options, and just play like the dealer).

By busting less, you decrease the house advantage and bring the likelyhood of winning closer to an overall 50/50. From there you can apply your player options and strategies - but at a much better position already.


Also, are you aware of what the house edges are with basic strategy? They are smaller than what you are talking about.
Yes, but if you did BOTH than you would surely be playing with a statistical advantage. YOU would have the edge.
 
#6
And in an attempt to verify the math, here's a slightly more comprehensive explanation of the statistical probabilities involved here.


Let's set up an imaginary game of blackjack - no player options or even betting strategies since they are irrelevant to the current calculation and can be added outside of the example to increase one's chances of winning.

This game of blackjack has one very special exception, however. In cases where the dealer and the player both BUST, it counts as a TIE.

Statistically, since both people are playing the exact same strategy, with the exact same gains and losses, and whenever they tie, nobody wins or loses, the chance of 'winning' in any given round of bets is 50%. If everybody could play blackjack from this position, adding card counting, player options, etc would only guarantee a profit at the end of the day (if you played long enough). The house advantage here is gone.


Now, the only difference that's relevant is the fact that in real life, if the dealer busts and you bust, the dealer still 'wins'. If we could minimize the chance of this happening, and bring the real life game closer to our fictional setup, then our chances of winning overall would be much much better. This is the purpose of playing four (or more) hands at once.
 

StudiodeKadent

Well-Known Member
#7
"Even without basic strategy..."

Basic strategy isn't exactly impossible to learn.... its actually pretty easy if you use the trainer on this site compulsively.

"Cutting the house advantage to 0.7868%..."

Basic strategy cuts the house advantage even lower (assuming you are playing a reasonable game) and doesn't require team play.

Therefore, basic strategy is both more convenient AND more effective than your technique (again, this is assuming your mathematics are correct... I don't want to spend the time looking at your calculations).

So why not just use basic strategy?
 

k_c

Well-Known Member
#9
snipe44 said:
then I guess I'm wrong? But where - can someone please explain :confused:

-------------------------
EDIT:

I think I've found one area where I'm wrong.

The chance that 3/4 people will bust with the dealer is not 0.28^4. That is the chance that one combination of those people will bust.

The number of combinations of 3 people, with 4 people at a table, is 4. So now we're up to:

0.28^4 * 4 = 2.458% chance of busting
+0.0017210368% (everyone busting) = 2.63%

but that's still better than the base percentage of 7.868%, right?!
This is the gambler's fallacy. Creative betting schemes do not alter the odds.

Take a simpler case. 7% bust rate, 1 or 2 hands.

.07*(-1)+.93*(0)=-.07 (1 hand, expected loss = .07 units)

(.07)*(.07)*(-2) = -.0098 (both bust, expected loss = .0098 units)
(.07)*(.93)*2*(-1) = -.1302 (1 bust, 1 does not bust, expected loss = .1302 units)
(.93)*(.93)*(0)= 0.00 (neither bust, break even)

-.0098-.1302+0.000 = -.14 (2 hands, expected loss = .14 units)

Player loses .07 of a unit for every hand he takes. It doesn't matter how many hands are added.
 
#10
StudiodeKadent:
Therefore, basic strategy is both more convenient AND more effective than your technique (again, this is assuming your mathematics are correct... I don't want to spend the time looking at your calculations).

So why not just use basic strategy?
I'm not saying don't use it. I'm saying, play with four people (they don't need to be smart, they just need to copy our strategy or listen to you). Or even play with four hands. This cuts down the house advantage. Then ADD all of your strategies and it will most likely raise your chances.

k_c:
I have to go out right now, but when I come home I'm going to work out the E(X) for the situation. I don't see any problems with your numbers so far, but something doesn't seem right about them.
 

shadroch

Well-Known Member
#11
"Mimic The Dealer" has a worse house edge than BS.
" Never Bust" has a worse house edge than BS.
It's impossible to use BS while also trying to "Mimic The Dealer"
and "Never Bust", but if you somehow could,it would still have a lower house edge than simple BS.
People with lots of fancy letters after their names, who actually make a living playing with numbers have been investigating ways to beat this game for at least fifty years, using the most sophisticated computers to aid them.
What would you guess the odds are of you coming up with such a simple strategy that everyone else has overlooked?
 

KOLAN

Well-Known Member
#13
snipe44 said:
I don't know if I should be saying this, but I just can't seem to see the flaw in how I've figured this out.

Okay, I read online (and it makes sense to me) that the source of the house advantage in Blackjack is the situation of double busting. If both you and the dealer play the same strategy, the house advantage comes from the fact that when you and the dealer bust (or would have both busted), the house gets the chips. If playing the dealer's strategy busts 28% of the time, then the starting house advantage without any strategy is 0.28 * 0.28 (when both you and the dealer bust) = 7.84% house advantage.

It is only because of player options like doubling down and splitting, that people have managed to reduce that number. However, I looked at that calculation (did a little subsequent empirical testing at home) and believe I have figured out a way to reduce the starting house advantage - before player options - to 0.7868...%

Answer: play in a team of four. Why?

Because then, the house advantage looks like this. If all of you bet the same amounts, and use the same strategy as the dealer (or at least as optimal statistically), then the house gains the advantage ONLY when 3 of you bust, or all 4 of you bust. This is because if the dealer busts and 1 or 2 of you bust, the other 2 or 3 people will win - and essentially cancel out the losses of players who busted. It becomes a team vs dealer TIE (or slight win).

So, back to our old calculation. The house advantage now comes when the dealer and 3 people bust, and when the dealer and 4 people bust.


0.28*0.28*0.28*0.28 = 0.00614656% (the chance that the dealer and 3 people bust)

0.28*0.28*0.28*0.28*0.28 = 0.0017210368% (the chance that everyone busts)

0.00614656% + 0.0017210368% = a total house advantage of 0.7868% (rounded)


So, now I'm here with my numbers and my hypothesis, looking for some discussion. The scientific method would be proud. I just hope that if I'm right, casinos don't change the game of Blackjack forever after seeing this =S.
mayby if you pla 4 hands and and wong in -1 and less, it is will by ++++
 

KOLAN

Well-Known Member
#14
shadroch said:
"Mimic The Dealer" has a worse house edge than BS.
" Never Bust" has a worse house edge than BS.
It's impossible to use BS while also trying to "Mimic The Dealer"
and "Never Bust", but if you somehow could,it would still have a lower house edge than simple BS.
People with lots of fancy letters after their names, who actually make a living playing with numbers have been investigating ways to beat this game for at least fifty years, using the most sophisticated computers to aid them.
What would you guess the odds are of you coming up with such a simple strategy that everyone else has overlooked?
i use never bust strategy +similar oscar betting strategy 1 evening i return all money which i lost in last months
 
#15
What would you guess the odds are of you coming up with such a simple strategy that everyone else has overlooked?
I'm simply testing the current scientific paradigm. If people didn't investigate things simply on the basis that 'smarter people out there haven't already figured out what you're trying to figure out', then science and society would be in a very poor place.

Re: Licentia

Thanks a lot for the support! It's nice to come across somebody who's willing to talk about actual numbers. What people like shadroch and kolan don't seem to understand about what I'm saying (and it may just be poor wording on my part) is that (I think) if you play with 4 hands, or 3 other people, then you reduce the house advantage to start with. From there, when you add all of your strategies, your chances are even better. I'm not saying "use this, not that" - quite the contrary. I'm saying, if you use this WITH your existing strategies, you could possibly have a greater than 50% chance at winning.

-------------------------------------------------------------

Here's some math. Please, everybody who knows what I'm talking about catch me if I'm wrong. Note: when I say worst case scenario, I mean: when you are player the dealer's strategy only.

1. If you look at the player's hand and the dealer's hand separately, in the worst case they each use the same strategy, they each have the same outcome distributions (chance of 17's, 18's, etc), and consequently the same chances to bust. Therein, like in my example, if in the case where both the player and the dealer busted it was counted as a TIE, the odds of winning a BJ game for the playing would be exactly 50%.

2. Therein, it is because of the case where both bust that the house has an advantage in real life. If we reduce the probability for a mutual bust, then the house advantage is subsequently decreased. That is the purpose of multiple hands. The calculations below should explain.

3. A normal blackjack game, worst case, with one player.

House advantage is equal to the chance that both the player and the dealer bust. The chance that either busts is 28%. Therein:

house advantage = 0.28 * 0.28 = 0.0784 (or 7.84%)

With that split, the players chances to win are: 50% - (7.84% / 2) = 46.08%
dealer's chances to win are: 50% + (7.84 / 2) = 53.92%

4. A blackjack game where you play 4 hands at once:

House advantage is equal to the chance that 3/4 players and the dealer bust, or 4/4 players and the dealer bust, because if one or two players and the dealer bust, then there is a net win (in the former) or a net tie (in the latter) since the players that don't bust will win back the chips lost by the busted players.

chance that 3/4 players and the dealer busts:
0.28 ^ 4 = 0.00614656 (or 0.615%) for every combination of 3 players
0.00614656 * 4 (only 4 combinations of 3 players in a 4 player group are possible) = 0.02458624 (or 2.46%)

chance that 4/4 players and the dealer busts:
0.28 ^ 5 = 0.0017210368 (or 0.172%)

2.46% + 0.172% = 2.632% house advantage

With that split, the player's chances to win before any strategy (in the worst case scenario) are = 50% - (2.632% / 2) = 48.684%

and the dealer's chances to win = 50% + (2.632% / 2) = 51.316%

---------------------------------

So, like I said in my edited post, it's not shaved to 0.7868% like I'd originally thought, but still -> 2.632% is still over a 5% difference closed!

EDIT: Also, I think I may be onto something. This may explain why the casinos (at least in my area) have a house rule that you must bet at least twice the minimum if you're going to play two hands at once, and as far as I can tell don't allow you to play more. Playing two hands will also decrease the house edge (by not as much, mind you) and so they rely on you draining your bank roll on a bad run (statistics are only really reliable in the long term).
 

KOLAN

Well-Known Member
#16
snipe44 said:
I'm simply testing the current scientific paradigm. If people didn't investigate things simply on the basis that 'smarter people out there haven't already figured out what you're trying to figure out', then science and society would be in a very poor place.

Re: Licentia

Thanks a lot for the support! It's nice to come across somebody who's willing to talk about actual numbers. What people like shadroch and kolan don't seem to understand about what I'm saying (and it may just be poor wording on my part) is that (I think) if you play with 4 hands, or 3 other people, then you reduce the house advantage to start with. From there, when you add all of your strategies, your chances are even better. I'm not saying "use this, not that" - quite the contrary. I'm saying, if you use this WITH your existing strategies, you could possibly have a greater than 50% chance at winning.

-------------------------------------------------------------

Here's some math. Please, everybody who knows what I'm talking about catch me if I'm wrong. Note: when I say worst case scenario, I mean: when you are player the dealer's strategy only.

1. If you look at the player's hand and the dealer's hand separately, in the worst case they each use the same strategy, they each have the same outcome distributions (chance of 17's, 18's, etc), and consequently the same chances to bust. Therein, like in my example, if in the case where both the player and the dealer busted it was counted as a TIE, the odds of winning a BJ game for the playing would be exactly 50%.

2. Therein, it is because of the case where both bust that the house has an advantage in real life. If we reduce the probability for a mutual bust, then the house advantage is subsequently decreased. That is the purpose of multiple hands. The calculations below should explain.

3. A normal blackjack game, worst case, with one player.

House advantage is equal to the chance that both the player and the dealer bust. The chance that either busts is 28%. Therein:

house advantage = 0.28 * 0.28 = 0.0784 (or 7.84%)

With that split, the players chances to win are: 50% - (7.84% / 2) = 46.08%
dealer's chances to win are: 50% + (7.84 / 2) = 53.92%

4. A blackjack game where you play 4 hands at once:

House advantage is equal to the chance that 3/4 players and the dealer bust, or 4/4 players and the dealer bust, because if one or two players and the dealer bust, then there is a net win (in the former) or a net tie (in the latter) since the players that don't bust will win back the chips lost by the busted players.

chance that 3/4 players and the dealer busts:
0.28 ^ 4 = 0.00614656 (or 0.615%) for every combination of 3 players
0.00614656 * 4 (only 4 combinations of 3 players in a 4 player group are possible) = 0.02458624 (or 2.46%)

chance that 4/4 players and the dealer busts:
0.28 ^ 5 = 0.0017210368 (or 0.172%)

2.46% + 0.172% = 2.632% house advantage

With that split, the player's chances to win before any strategy (in the worst case scenario) are = 50% - (2.632% / 2) = 48.684%

and the dealer's chances to win = 50% + (2.632% / 2) = 51.316%

---------------------------------

So, like I said in my edited post, it's not shaved to 0.7868% like I'd originally thought, but still -> 2.632% is still over a 5% difference closed!

EDIT: Also, I think I may be onto something. This may explain why the casinos (at least in my area) have a house rule that you must bet at least twice the minimum if you're going to play two hands at once, and as far as I can tell don't allow you to play more. Playing two hands will also decrease the house edge (by not as much, mind you) and so they rely on you draining your bank roll on a bad run (statistics are only really reliable in the long term).
2 players bust 1 win 1 tie
200 player bust 100 win (it is not 101win) 100 tie
results same
i think you vrong in Tie
 
#17
2 players bust 1 win 1 tie
200 player bust 100 win (it is not 101win) 100 tie
results same
i think you vrong in Tie
I'm sorry, I don't think I understand. Please elaborate (and tell me what part of my calculations it pertains to).


I would like to note a general undertone of the responses here. People seem to be disregarding the fact that the only statistical advantage the house has over the player, is the situation when dealer AND player bust. The replies I'm seeing only look at player busts, and that is not what I'm talking about.

Yes, the player busts sometimes and the dealer wins with a hand <= 21. Also, sometimes the dealer busts and the player wins with a hand <= 21. The point is that the probability of either happening is EXACTLY THE SAME! That's why in the calculations I've been leaving out those situations - they're irrelevant. It's the situation when both bust, that skews the 50/50 chance of winning.

Licentia:
Now, working from this .5 or less edge, could playing 4 hands balance out the wins and losses?
If my calculations are correct, from there it would put you at a chance to win of about 51.3%! a 2.1% spread against the house. It's unbelievable
 

QFIT

Well-Known Member
#18
It is irrelevant how many other players there are and what they do. Dealer bust rate is not a useful number. You are on the wrong track.
 

KOLAN

Well-Known Member
#19
snipe44 said:
I'm sorry, I don't think I understand. Please elaborate (and tell me what part of my calculations it pertains to).


I would like to note a general undertone of the responses here. People seem to be disregarding the fact that the only statistical advantage the house has over the player, is the situation when dealer AND player bust. The replies I'm seeing only look at player busts, and that is not what I'm talking about.

Yes, the player busts sometimes and the dealer wins with a hand <= 21. Also, sometimes the dealer busts and the player wins with a hand <= 21. The point is that the probability of either happening is EXACTLY THE SAME! That's why in the calculations I've been leaving out those situations - they're irrelevant. It's the situation when both bust, that skews the 50/50 chance of winning.

Licentia:


If my calculations are correct, from there it would put you at a chance to win of about 51.3%! a 2.1% spread against the house. It's unbelievable
count again you mist samthing
dealer player bust 50/50 here you frong it is not tie it is you lost
 
#20
It is irrelevant how many other players there are and what they do. Dealer bust rate is not a useful number. You are on the wrong track.
Then an important question remains: what is the source of the house advantage in black jack?


count again you mist samthing
dealer player bust 50/50 here you frong it is not tie it is you lost
I was using a fictional situation where a mutual bust is counted as a tie, to illustrate the fact (I believe) that the house advantage comes solely from situations where both dealer and player bust. From there, I established that in the fictional setup, the chances of winning were 50/50 (are they not? if so, why?), and added the reality of it NOT being a tie at the end (to calculate the house edge).
 
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