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

[London Colin]

And, welcome aboard at BJInfo!

Thanks Ken.

Hope I got my maths right. Unlike you and k_c, I went along with the idea of ignoring all but the mutual busts, on the basis that everything else balances out, which I think does make sense (in this limited scanario of 1:1 payoff for a natural, and mimic-the-dealer strategy).

Snipe44,

I should point out that I'm not much of a mathematician, and my starting point was just a general understanding of the fundamentals that people have been attempting to hit you over the head with in this thread , plus a rough idea of how to go about doing the necessary calculations to demonstrate those fundamentals in action in this particular example.

I think it's fair to say you fell into the trap of taking the results of a faulty calculation and being so wedded to them that you let them lead you to all manner of fanciful conclusions which, if you had been presented with them 'cold', you would probably have seen the logical impossibility of straight away.

For instance, it ought to be obvious that a team of players, or a single player playing multiple hands, cannot magically expect to take more money from a BJ table than a random group of players who just happen to sit down together. Whatever the reason for a casino to make you bet more if you split to two hands, it's not to recoup some lost house edge!

 

[QFIT]

A simple, non-math, way of putting it:

If you bust, it doesn't matter what the dealer does. If you do not bust, it doesn't matter what the other players do since the dealer must play.

All that matters is the rate at which the dealer busts against YOU. And that is not the overall dealer bust rate nor is it affected in any way by other players.

 

[stophon]

To get the odds of a 3:2 blackjack game playing dealer strategy, you would calcuate
Odds you bust * odds dealer bust + Odds blackjack * .5
Correct?
I calculate a 5.427% house edge with this strategy.

Edit: nevermind Ken already answered my question in an earlier post

 

[QFIT]

You guys have got to get off this "bust" kick. Bust rate is not a part of advantage calculation. It completely ignores the hands where nobody busts.

 

[Licentia]

They are only "unintuitive" to non-mathematicians. This thread is filled with complete nonsense. Ignore bust rate. This stat is used in thousands of stupid gambling systems created over centuries. It has no use. There is a reason that casinos have made billions for centuries. There is no easy method of beating them.

Can you provide some names/descriptions of these "thousands" of particular "stupid gambling systems" so we can search them on-line and refer to them?

Licentia

 

[Katweezel]

Snipe44, I understand exactly what your argument is. Unfortunately, it's not right, so let's see why.

Yes, the entire house edge in blackjack is due to the "double bust" scenario, where both the player and the dealer bust. (The players loses anyway.)

OK, let's backtrack to snipe44's mythical game, we'll call it EvenJack.
The player and dealer both must play Stand on all 17s strategy, and the double bust is a tie. Snipe44 left out an important rule change that is necessary to even the game. Blackjacks must pay even money, not 3:2. It should be apparent to most that this is an even game, with a house edge of 0%.

Now, let's switch to the normal rules where if the player busts, they lose regardless, even if the dealer also busts. The house edge here is indeed the 0.28 * 0.28 = ~ 7.84% (If blackjack pays 3:2 for the player, the house edge is approximately 5.5%. I mention this because some books have published the house edge for a Mimic the Dealer strategy.)

It's better if we break it down this way though:

Player and Dealer bust: 0.28 * 0.28 = 7.84% of the time. (Player loses)
Player busts, and dealer does not: 0.28 * 0.72 = 20.16% of the time (Player loses)
Player does not bust, dealer busts: 0.72 * 0.28 = 20.16% of the time (player wins)
Neither player nor dealer bust: 0.72 * 0.72 = 51.84% of the time (player wins half, dealer wins half)

Player's expectation = -7.84% -20.16% + 20.16% + (51.84%/2) - (51.84%/2) = -7.84%

With two players, what happens?

When the dealer busts (28% of the time),

• Both players bust (0.28 * 0.28 = 7.84%) [-2 units]
• Both players do not bust (0.72 * 0.72 = 51.84%) [+2]
• Player 1 busts, player 2 not (0.28 * 0.72 = 20.16%) [Tie]
• Player 2 busts, player 1 not (0.72 * 0.28 = 20.16%) [Tie]

When the dealer does not bust (72% of the time),

• Both players bust (7.84%) [-2]
• Both players do not bust (51.84%) [1/4 of time +2, 1/2 time tie, 1/4 of time -2] Avg = 0
• Player 1 busts, player 2 not (20.16%) [1/2 of time -2, 1/2 time tie] Avg = -1
• Player 2 busts, player 1 not (20.16%) [1/2 of time -2, 1/2 time tie] Avg = -1

Ignoring the lines that are ties, here are the results:
28% * 7.84% * -2 = -0.043904
28% * 51.84% * +2 = +0.290304
72% * 7.84% * -2 = -0.112896
72% * 20.16% * -1 = -0.145152
72% * 20.16% * -1 = -0.145152

Add up the 5 lines, and you get an expectation of -0.156800 for the two players. Divide that by the 2 units bet, and you get, predictably, the same player expectation of -7.84%.

Two players fared exactly the same as one player did. The same is true for 3 or 4 players, though the math gets tedious.

-7.84%... isn't that very close to the figure for the dealer edge for BJ (without rules like splits, doubles and BJ?) Don S takes credit for discovering the player bust rate figure which is around 15.75% (or near) V dealer bust figure of 28.20%. The difference looks like around 12%, quantifying the 'must go first' disadvantage?

Now Ken, your figures are for both players set on 28%. What happens when one (the dealer) is set on 28%, but the player is set on his 'normal' bust figure of 15.75%?

 

[UncrownedKing]

-7.84%... isn't that very close to the figure for the dealer edge for BJ (without rules like splits, doubles and BJ?) Don S takes credit for discovering the player bust rate figure which is around 15.75% (or near) V dealer bust figure of 28.20%. The difference looks like around 12%, quantifying the 'must go first' disadvantage?

Now Ken, your figures are for both players set on 28%. What happens when one (the dealer) is set on 28%, but the player is set on his 'normal' bust figure of 15.75%?

This the first post of yours I read that didn't include sarcasim.

 

[Katweezel]

Voodoo, WooWoo

You guys have got to get off this "bust" kick. Bust rate is not a part of advantage calculation. It completely ignores the hands where nobody busts.

Norm, here are some of your other quotes on this thread on the subject of dealer busts:

"This thread is filled with complete nonsense. Ignore bust rate".

"EV is calculated by simulation (or combinatorial analysis if fixed rounds are played). You must generate a strategy based on all rules. You are trying to pretend that all that matters is bust rate. Bust rate is a small part of hit/stand, double, split, surrender and insurance decisions. What matters is if you win the hand. Why would you think this is totally based on bust rate of the dealer? You are trying to win, not bust the dealer. You can win without the dealer busting. If you want to increase the dealer bust rate, this is easy. Never hit. The dealer bust rate will increase. But, you will lose your shirt."

"A simple, non-math, way of putting it:
If you bust, it doesn't matter what the dealer does. If you do not bust, it doesn't matter what the other players do since the dealer must play."

"All that matters is the rate at which the dealer busts against YOU. And that is not the overall dealer bust rate nor is it affected in any way by other players."

I appreciate your input Norm.
Say there are 6 players; 5 and the dealer; about to begin a 6-deck shoe, which may have about 16 rounds. The dealer bust rate is 28.20%, the player bust rate around 15.75% ... long term average figures. If I am one of these 5 players and I look at the dealer about to begin, I expect her to bust 4 or 5 times - average rate. Hopefully, she will bust a lot more than her expected average, if it is my lucky night.

So is this thinking fatally flawed here? In other words, why should I ignore a very-high figure of 28.20% for dealer busts. (And this is without getting into the very-lucrative prime Voodoo talent of steering a dealer bust. WooWoo.)

 

[QFIT]

The dealer bust rate varies by the number of players and by the way they play. But neither the number of players nor the way they play affects your edge. That makes the bust rate meaningless. Bust rate is based on variables that are irrelevant to your edge. BJ is a game between the dealer and the player. The only affect of other players is to slow down the game.

 

[Katweezel]

This the first post of yours I read that didn't include sarcasim.

Dear UncrownedYetKing, nice to see your developing sense of humor is coming along just fine. Keep up the good work. And BTW, it's spelled, sarcasm. [Now that was sarcasm.]

 

[CORed]

then I guess I'm wrong? But where - can someone please explain

-------------------------
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?!

Because not busting doesn't necessarily mean that you win.

The biggest mistake in your calculations is that you seem to be assuming that not busting means an automatic win.

 

[ExhibitCAA]

No, I think the biggest mistake of his calculation was that he ignored the fact that when N players bust, THEY LOSE $N, not $1.

 

[ycming]

According to: http://wizardofodds.com/blackjack

Mimic the dealer: For my analysis of this strategy I assumed the player would always hit 16 or less and stand on 17 or more, including a soft 17. The player never doubled or split, since the dealer is not allowed to do so. This "mimic the dealer" strategy results in a house edge of 5.48%.

So really playing 4 hands with mimic the dealer is the road to busting out ..

Ming

 

[yolev]

The bottom line is..........

The dealers advantage (and it's a great one) is that you (the player) finishes your hand always before the dealer. This advantage trumps any card playing hit or stand strategy period.

 

[ExhibitCAA]

Everybody here understands that, including the original poster. His question is, what is the flaw with his argument that this double-bust advantage can be nullified by employing four spots. For those who looked at this question (instead of telling the poster that the house's double-bust edge is mitigated by the 3:2 bonus on naturals and other improvements to mimic-the-dealer), it seems that there were errors in the arithmetic, including not counting the full amount lost when several of the four players bust. The economic argument is also strong--the game doesn't know which players are sharing money. Chips in the circle are chips in the circle, so there is no difference between a person playing four spots and a random assortment of four strangers. If the system worked, the four strangers would win money collectively from the casino; whether they then go home and share the profits is irrelevant if our only question is whether the casino was beaten.

 

[Frankie]

Wait, wait. I've got it all figured out. Dealer busts 28% of the time, right? Well then if you never hit anything above 11, then 28% of the time your 4 people will win 4 bets.

But if they can win 25% of the time they breakeven, because remember they win all 4 bets. So this is a 3% PLAYER advantage.

^^^^^^^
This reasoning is about equally inane as the OP. I read this post weeks ago and still get a chuckle out of it.

And by the way, I love the fight over "his biggest error." Because the errors are too numerous to mention. And some of them worked the othe way (i.e., he ignored that sometimes player may beat the dealer without dealer busting). Basically he just took a few numbers out of thin air, which had no relevance whatsoever, added them together and tada. You can't really fight over what he missed. He missed everything.