Dealer 2 or 3 showing.

[UK-21]

Does anyone have any stats on the %age of times that the dealer will bust out / make a hand when their card showing is a 2 or a 3?

Interested in the impact of hitting a 12 against these two at higher counts. 12v3 and 12v2 are both included within the I18, so the advantage of standing on the 12 at the correct TC must be reasonably significant (as opposed to all of the index plays that are not included which are pretty insignificant?).

Thanks.

 

[ycming]

hmm isn't I18 based on the indicies which brings the highest EV combining with the frequency they occur?

Up Card Expected
Value
2 9.10%
3 12.38%
4 15.85%
5 19.65%
6 23.40%
7 14.40%
8 5.82%
9 -4.06%
10 -17.36%
A -33.78%

From wizzard of odds, notsure if it is any help..

ming

 

[daddybo]

Does anyone have any stats on the %age of times that the dealer will bust out / make a hand when their card showing is a 2 or a 3?

Interested in the impact of hitting a 12 against these two at higher counts. 12v3 and 12v2 are both included within the I18, so the advantage of standing on the 12 at the correct TC must be reasonably significant (as opposed to all of the index plays that are not included which are pretty insignificant?).

Thanks.

Try here.

http://wizardofodds.com/blackjack/appendix2.html

 

[Jack_Black]

okee dokee. so given the probability and unlikelihood that the dealer busts with an Ace up, why do the BS cards all say to DD when you have an 11?

 

[creeping panther]

Uk

Does anyone have any stats on the %age of times that the dealer will bust out / make a hand when their card showing is a 2 or a 3?

Interested in the impact of hitting a 12 against these two at higher counts. 12v3 and 12v2 are both included within the I18, so the advantage of standing on the 12 at the correct TC must be reasonably significant (as opposed to all of the index plays that are not included which are pretty insignificant?).

Thanks.

2up bust=35%

3up bust=37%

CP

 

[21gunsalute]

okee dokee. so given the probability and unlikelihood that the dealer busts with an Ace up, why do the BS cards all say to DD when you have an 11?

That's only for H17 games and it's because you have a very small advantage. If you're counting cards and the count is high it becomes much clearer. You know the dealer doesn't have a 10 for 21 and there's a good chance you will receive a 10 for 21.

 

[Canceler]

As 21gunsalute alluded to…

okee dokee. so given the probability and unlikelihood that the dealer busts with an Ace up, why do the BS cards all say to DD when you have an 11?

Any strategy based solely on dealer/player bust rates fails to consider who is likely to have the best hand when neither busts.
But I’m sure you knew that.

 

[ycming]

I think more importantly, could someone post up, the advantage you will gain if you know exactly what dealer's up card going to be?

And the advantage you will gain, knowing exactly which first card you will get 7/8/9/10/A ?

Well i know ace gives you a massive 43% advantage

Ming

 

[nottooshabby]

I think more importantly, could someone post up, the advantage you will gain if you know exactly what dealer's up card going to be?

And the advantage you will gain, knowing exactly which first card you will get 7/8/9/10/A ?

Well i know ace gives you a massive 43% advantage

Ming

From "The Theory of Blackjack":

Player's Advantage when dealer exposes:
2: 10%
3: 14%
4: 18%
5: 24%
6: 24%
7: 14%
8: 5%
9: -4%
10: -17%
A: - 36%

Player's Advantage when his first card is:
2: -12%
3: -14%
4: -16%
5: -19%
6: -18%
7: -17%
8: -9%
9: 0%
10: 13%
A: 52%

 

[daddybo]

I think more importantly, could someone post up, the advantage you will gain if you know exactly what dealer's up card going to be?

And the advantage you will gain, knowing exactly which first card you will get 7/8/9/10/A ?

Well i know ace gives you a massive 43% advantage

Ming

If you knew in advance of placing a bet the dealers up card and the players up card; then realistically off the top of my head, I would guess the advantage would be in the 60-70 percent range. You wouldn't even bet unless your upcard was strong and the dealers was weak.

 

[ycming]

If you knew in advance of placing a bet the dealers up card and the players up card; then realistically off the top of my head, I would guess the advantage would be in the 60-70 percent range. You wouldn't even bet unless your upcard was strong and the dealers was weak.

This happens alot on S17 games where i play. It has been several times, the ace/ten has been pulled by mistake when dealer had S17 or when I had blackjack everyont busted but the dealer continouses to take card for himself (ENHC am playing).

It is rather tasty, max betting the box when i know my next card is an ace .

Am i right that betting kelly, if you knew your advantage is 13% you would bet 13% of your bank roll?

Thanks
Ming

 

[assume_R]

Am i right that betting kelly, if you knew your advantage is 13% you would bet 13% of your bank roll?

Yeah, if you're betting full kelly, but some people prefer to bet half kelly (or 6.5% of their bankroll on that 13% advantage).

Also remember that kelly betting would say bet 0% of your bankroll at negative counts, and playall means you have to slightly overcompensate.

 

[UK-21]

Popping back to the original base of the thread, it's the 12v2 play I'm looking at. The index to stand on a 12v2 is at TC+3 (hi-lo - according to Wong and DS).

Assuming that all three of the additional high cards are 10s, this would mean (with an averaged distribution) if you hit the 12 you'd have a 19/52 or 37% chance of catching a 10 and busting. If you stand on a 12 you're relying on the dealer busting out to win the hand, and on the figures offered by CP there's only a 35% chance of this happening - 65% of the time the dealer will make a hand and win. So it's a tight call.

If you assume that only 2 of the additional three cards are tens, and the other's an ace, the chances of drawing a ten and busting reduce to 18/52 or 35%, so there's nothing in it.

The above examples are based on average distribution, and of course don't take into account the concentration of 7,8,9s which are not counted but which will turn a 12 into a likely winning hand (and on an assumed averaged distribution they still make up 12/52 of the deck).

Question is:
Bearing in mind that at TC+3 if you stand 12v2 you're likely to lose, why not hit it? - there's a 63% of not busting and a 23% chance of ending up with a 19,20,21. If you pull a small card and don't bust, it also reduces the chances slightly of the dealer getting one and thereby increases the chances slightly of them pulling a 10.

or alternatively,

Move the index to a higher point. At TC+6, assuming all additional high cards are tens, hitting a 12 will carry a 22/52 or 42% chance of busting which is considerably higher than the 35% chance of the dealer busting. Where do you make the switch? At TC+3 it's 37%, at TC+4 38%, at TC+5 40%, all assuming that the additional cards are 10s. As the TC creeps up though, the likelihood is that they won't all be. This also doesn't take account of the impact on longer term EV if you ramp up or double the wager between TC+3 and TC+4.

The 12v2 at higher counts situation comes up for me with monotonous regularity, and I've always wondered just how much advantage is gleaned from standing and relying on the dealer to bust out - which they never seem to do.

Comments ?

 

[Sucker]

If you knew in advance of placing a bet the dealers up card and the players up card; then realistically off the top of my head, I would guess the advantage would be in the 60-70 percent range. You wouldn't even bet unless your upcard was strong and the dealers was weak.

Unless your first card happens to be an ace, you couldn't come anywhere near this advantage. For example; if your first card is a ten and the dealer's up card is a 5, your advantage is 34%.

As far as whether or not to bet full Kelly; if your first card is a ten, then your optimal bet size IS full Kelly, or 13% of your BR. This is the ONLY time in BJ where full Kelly is correct. This is because when your first card is a ten , you can't get a card with it to give you a double down, so the most you can possibly risk on this hand IS 13% of your BR, and no more.

The reason most blackjack players (correctly) use half Kelly or less, is BECAUSE of double downs & splits. The classic example of why full Kelly is not correct in the game of blackjack: Supposing you're an ace tracker. If you bet 50% of your bankroll, one out of 17 times (single deck) you're going to get TWO aces. If you split them, you'll be risking your ENTIRE BR on one hand. You are 100% CERTAIN to tap out, sooner or later.

 

[daddybo]

Unless your first card happens to be an ace, you couldn't come anywhere near this advantage. For example; if your first card is a ten and the dealer's up card is a 5, your advantage is 34%.

How do you get a 34% player advantage with a player 10 vs dealer 5? I get more like 63% advantage. Maybe we are looking at this differently. I am including both player cards, since the player either has them both down or up.

Also.. I get an average advantage of around 80% against the 5 for all two card hands containing a 10 against the 5... that sounds high, I need to go back and check that one.

 

[Nynefingers]

Unless your first card happens to be an ace, you couldn't come anywhere near this advantage. For example; if your first card is a ten and the dealer's up card is a 5, your advantage is 34%.

As far as whether or not to bet full Kelly; if your first card is a ten, then your optimal bet size IS full Kelly, or 13% of your BR. This is the ONLY time in BJ where full Kelly is correct. This is because when your first card is a ten , you can't get a card with it to give you a double down, so the most you can possibly risk on this hand IS 13% of your BR, and no more.

The reason most blackjack players (correctly) use half Kelly or less, is BECAUSE of double downs & splits. The classic example of why full Kelly is not correct in the game of blackjack: Supposing you're an ace tracker. If you bet 50% of your bankroll, one out of 17 times (single deck) you're going to get TWO aces. If you split them, you'll be risking your ENTIRE BR on one hand. You are 100% CERTAIN to tap out, sooner or later.

I was under the impression that the correct Kelly bet was adjusted for variance, so for example if you are playing at some true count such that your edge is 2%, you would not bet 2% of your bankroll, but something closer to 1.5%. I forget the exact multiplier, but it's around 75% of your advantage, give or take a few percent. As you said, this accounts for the fact that you will sometimes win or lose more than one unit. But I don't think that using half Kelly bets has anything to do with doubles and splits, as the Kelly bet already factors those in. Fractional Kelly betting is less than optimal, but it is much easier to stomach the variance and you will be forced to adjust your bet sizes (bet ramp) less frequently.

I don't recall the proper strategy for the situation where you know your first card is an ace, but I know Grosjean has an article that discusses it.

 

[Sucker]

I was under the impression that the correct Kelly bet was adjusted for variance, so for example if you are playing at some true count such that your edge is 2%, you would not bet 2% of your bankroll, but something closer to 1.5%. I forget the exact multiplier, but it's around 75% of your advantage, give or take a few percent. As you said, this accounts for the fact that you will sometimes win or lose more than one unit. But I don't think that using half Kelly bets has anything to do with doubles and splits, as the Kelly bet already factors those in.

Full Kelly is the optimal bet size for an even money game where you can ONLY win or lose one bet, and variance IS figured into the formula.

However; you ARE correct; the optimal bet size for a BLACKJACK game is much closer to 3/4 Kelly, and this has everything to do with the fact that it's not always an even money game.

What I was trying to say was that in this one special case, when you know that your first card is a ten, you ARE playing an even money game and your OPTIMAL bet size SHOULD be full Kelly. Whether or not you chose to bet it that way is really just a matter of personal preference, for this reason:

Fractional Kelly betting is less than optimal, but it is much easier to stomach the variance and you will be forced to adjust your bet sizes (bet ramp) less frequently.

I agree 100% with your statement about the variance sometimes being very hard to stomach, and for this reason; most blackjack players, myself included, prefer to play blackjack using something closer to 1/2 Kelly. There's probably nothing more disheartening than to work your butt off for a month, build a nice chunk of BR, and then lose it all back in just a few hours of perfect play, or as in the case of an exposed paint card; one hand!

 

[Sucker]

How do you get a 34% player advantage with a player 10 vs dealer 5? I get more like 63% advantage. Maybe we are looking at this differently. I am including both player cards, since the player either has them both down or up.

Also.. I get an average advantage of around 80% against the 5 for all two card hands containing a 10 against the 5... that sounds high, I need to go back and check that one.

Using my BJ simulator, and playing single deck, I gave myself a 10 as my first card and gave the dealer a 5. After running one million hands, I won 647,702, lost 330281; and pushed 62220. I got 80406 blackjacks. This works out to be a player's advantage of about 34%.

 

[Nynefingers]

Full Kelly is the optimal bet size for an even money game where you can ONLY win or lose one bet, and variance IS figured into the formula.

However; you ARE correct; the optimal bet size for a BLACKJACK game is much closer to 3/4 Kelly, and this has everything to do with the fact that it's not always an even money game.

We are in agreement with regard to what the optimal bet is, but we disagree over the name for it, which is really not a big deal. I just thought that the bet of 3/4 of your advantage in BJ was actually still considered full Kelly, and therefore half Kelly would be 3/8 of your advantage, for example. I thought that the Kelly bet was defined as the optimal bet (for maximum rate of geometric bankroll growth) for a wager with a given payout distribution, without even money payout being a condition. You are saying even money payout is a condition. It doesn't change what is the "correct" bet, it just changes the name for it. Where it does matter is if you start talking about betting 1/2 Kelly or .3 Kelly or some other fraction, which would we would interpret differently. I don't know which is correct, but I'm not to worried about it, TBH

What I was trying to say was that in this one special case, when you know that your first card is a ten, you ARE playing an even money game and your OPTIMAL bet size SHOULD be full Kelly.

Strictly speaking, this is not purely an even money game, as there is a chance for blackjack. Also, we're back to the disagreement over the correct words to describe the optimal bets. And again, I'm not worried about it. We agree about the important stuff :grin:

 

[daddybo]

Using my BJ simulator, and playing single deck, I gave myself a 10 as my first card and gave the dealer a 5. After running one million hands, I won 647,702, lost 330281; and pushed 62220. I got 80406 blackjacks. This works out to be a player's advantage of about 34%.

We are talking about two different things. You are correct in saying play all hands with a 10 vs the dealer 5 is about 34% advantage. I was originally saying to NOT play the weak hands, but to only bet the strong hands against the 5. I.E. If you knew your hand in advance and knew the dealers card would always be a 5. You would bet only when you had a positive EV hand. I don't think I made that clear.