Odds of Dealer Busting at Different Counts

I use Hi-Lo. My local casino has electronic blackjack that is dealt out of a 6 deck shoe that reads the cards as they come out. So, normal shuffle, normal dealing, but electronical tracking of play. It's called Chipless blackjack.

When you are dealt your first two cards, and the dealer's up card, you then have the option of placing a side bet on whether you will win your hand. You can bet the same amount as your original bet, and it will pay based on odds that differ based on what your first two cards and the dealer's up card are. So, for instance, if you have bet $10, you can bet another $10 at this time, and if you have two 10s versus a dealer's 6, it will pay like $0.46. But, if you've got a 16, versus a dealer's 10, it will pay like $30 (not sure of the numbers right now, but I know that they don't differ for given cards. ie: they are not being adjusted based on the count).

So, I'd like to know the odds of the dealer busting, for each up card, at different counts. Anyone got this info?

Don't you want to know the odds of winning each hand combination vs. the dealer's upcard, regardless of whether he busts or not, by count? :-)

Will have to look around. Norm may have this, but it requires a huge matrix.

Don

You are exactly right. I don't know why I said just busting.

I recall a graph of bust %age by count for various upcards on Norm's site. Now, it's just a matter of finding it.

the bust rate really didn't change all that much at higher counts. Much less than I was expecting. Almost an insignificant change. The real advantage comes from the player blackjack and the 3-2 payout and that begins to happen a little more frequently in higher counts. Double downs also become more profitable at higher counts, but that is a distant second to the blackjack 3-2 payout as far as where the small advantage at higher counts really comes from.

The overall bust rate of the dealer for all upcards changes very little with the count. But, the bust rate, per each individual upcard can change significantly with varying counts.

Don

The bust rate for 6 up is 42%. It goes up to 46% or so at very high counts. I don't consider that dramatic. What cards have dramatic changes by count?

I'm reasonably sure that, in a shoe game, a 6 busts over 50% of the time with trues of +9 or +10. In single deck, it busts > 50% by TC = +5.

Don

I researched this a few years ago when a bust sidebet surfaced. I''m sure it never reaches 50%, even at +10.

Found Norm's chart: http://www.blackjacktheforum.com/entry.php?5-Dealer-Blackjack-Bust-Rates-by-Count-and-Upcard

If it goes from 42% to 46% that's almost a 10% increase in the rate of busting. I'd call that significant. If, say, the side bet is operating on a house edge of 5%, then this could make the side bet profitable for the player.

According to my CA-program (infinite decks),the bust rate for a Six is 48.6% at TC+10 compared to 42.3% for a neutral deck.
Only the Five gets over 50% (50.5% for TC+10)compared to 41.6% for neutral.
The six doesn't get that high because of the Ace-effect.

Francis Salmon

The 5 and 6 bust pay 1:1, so 50% is the break-even point. Not profitable.

"According to my CA-program (infinite decks),the bust rate for a Six is 48.6% at TC+10 compared to 42.3% for a neutral deck."

I accept that as correct. Doesn't exactly make me a liar! :-)

"Only the Five gets over 50% (50.5% for TC+10)compared to 41.6% for neutral."

May have confused the two. I was sure that there was a dealer upcard that broke 50% of the time at TC > +10.

What about fewer decks?

Thanks.

Don

Since all we get in Europe are shoe games, I didn't have any incentive to analyse singe deck.
But when I look at the table on page 149 of Griffin's Theory of Blackjack, I don't see how the dealer Six can bust over 50% of the time at TC+5 - nor the Five.

Francis Salmon

I'm not sure what the payoffs are, but they are dependent on the dealer's up card AND your first two cards. The bet is placed after you get your two cards. So, if you've got two 10s, and the dealer has a 6, and your original bet is $10, you can bet another $10 on this bet, and it would pay like $0.46. But, if your first two cards are, say, a 10 and a 6, then the bet pays over 1:1 (I'm not sure exactly, but I will be making another trip in a few days, and I'll report back). But, it will be difficult, as there are different payouts for every combination of player's two cards and dealer's up card.

In the case of 20 against Six which pays $0.46 for a 10$bet the payout is too small. There is roughly a 10% chance that the dealer will make 21 and another 10% that there will be a stand off. So on a hundred of such situations you get paid 80*0.46 = $36.80 but you lose 10*10 =100$ leading to a net loss of $63.20. In other words, this bet has an ev of -6.32%.
To ensure roughly the same margin, I expect the pay out for a stiff to be $12 (against the Six).If that's the case,then in order to turn the odds in your favour by counting cards, you would need a TC of +6.
Conclusion: The favorable situations will probably be too rare to make this bet exploitable.

Francis Salmon

It was surprising how hard it was for me to get actual numbers, and record them, while I was counting. I was overmatched. Anyway, here are a couple:
Two Tens vs. a dealer's 6 pays $0.86 for a $10 bet.
15 vx dealer's 5 pays $13.17 for a $10 bet.

I will gather more, but you can't just watch, because you've got to be playing for the odds to show up for you, and it's hard to just watch someone else' monitor. I think I remember a 12 vs. dealer's 6 being something like $15 for a $10 bet, but that's approximate.

Even in a neutral count paying $15 for winning with 12 versus 6 would be very favorable for the player. With a bust rate of 42%, the calculation would be as follows:
42*15-58*10=+$50 for a hundred such situations (ev +5%)
The other odds that you indicated are still slightly favorable for the bank but might turn around in a positive count.
Are you sure that the payouts don't change with the count?

Francis Salmon

The $15 might have been wrong. I will make more of an effort to get absolutely correct payout numbers in the next week. I'm creating a form that I can fill out while at the casino.