Bankroll management

Bankroll management

Hello,
I�ve got an idea how to beat a local blackjack game playing basic strategy and using a bonus offer. The game is European (no hole card) 6-deck blackjack, but the rules are good - dealer stands on soft 17, double on any 2 cards, double after split, resplit aces, early surrender versus 10. The house edge is about 0.24%, but to be conservative let me round it to 0.5%. At the moment there is the following bonus running: if one places a 10 unit bet and receives as an initial hand a pair of sevens he is entitled to 50 units in free bets. The player may use the free money as he pleases, but to be able to cash the money out he must increase it in amount to 100 units at least. The probability of getting a pair of sevens for 6-deck game is about 0.54%. The above percentage shows that from every 185.2 initial hands there should be one with a pair of sevens. I�ll round 185.2 to 200. Thus, for every 200 initial hands of 10 units the basic strategy player will lose 200*(10/0.76)*0.005=13.16 units. I divide 10 by 0.76 to include extra money on doubling and splitting. On the other hand, for every 200 hands, on average, the player will be rewarded with 50 units free money. If one places all the 50 units on the next hand and win he will turn the money into 100 units. Thus he will be able to cash the 100 units out. When betting with free money one can neglect surrendering, splitting and doubling options and still should be able to win about 45% of these hands excluding ties (100%=45% winning hands + 55% losing hands). Here are the calculations:

Probability
0.45
Possible outcome
86.84=(-13.16)+100
Product
39.08=0.45*86.84

Probability
0.55
Possible outcome
-13.16
Product
-7.24=0.55*(-13.16)

Expected Value=39.08+(-7.24)=31.84
Player�s edge=31.84/(200*(10/0.76))=0.012=1.2%

A dream-come-true. But what about the standard deviation? One could lose much more than just 13 units for 200 hands and could wait much longer than 200 hands for a pair of sevens. And he could lose his first 5-6 free money bets. So, what is the worst I can expect? What amount of bankroll will I need and how long will I have to play to overcome the effect of standard deviation? It will be very kind if somebody gives me a piece of advice on this matter.

Advice

Side count sevens.

By the way

If you play perfect BS, no need to round up to 0.5%. Why not just use the correct value? Also, the division by 0.76 is wrong. The edge that's quoted is based on initial bets. You don't adjust for the extra money for splits and doubles. If you did, we'd all quote a different (smaller) house edge, based on a larger amount bet. So, you're thinking too much! :-)

Don

To anonimuss

Thanks for your advice. Side-counting of 7s obviously increases the probability of 7-7 quite a bit. I'll consider it.

To Don Schlesinger

Dear Sir,
Thank you for advice and encouragement. So, Blackjack Attack!

Questions about the "free money"

Blackjack Rookie,

Let's say you want to play 50 units "free money" along with 50 units of "real money" (since you said you have to at least match the free money portion of the wager).

If you win your free money bet (say without DD, splitting, or getting a BJ), what happens:

(a) You receive 150 units and the house takes away the free money, or
(b) You receive 100 units and you keep the free money for another play, or
(c) You receive 100 units and the house takes away the free money?

What happens if you choose to surrender? Do you:

(a) lose 50 units of free money only, or
(b) lose 25 units of free money and 25 units of real money, or
(c) lose 50 units of real money only, or
(d) lose 50 units of free money and lose 25 units of real money?

How about doubling down... do you DD with 100 units of real money, or only 50 units?

What happens on a split... does the second hand need 100 units of real money, or only 50 units?

If you get a BJ, are you paid 150, or only 125?

On a push, do you get to keep the free money?

The edge you get for this depends on these answers. Post your answers and I'll see what I can figure.

Dog Hand

Also, as anonimuss correctly indicated, keeping a sidecount of 7's would be quite valuable here.

About the "free money"

Hello,
Thanks for you readiness to help. It�s not necessary to match the �free money� wager with a wager of �real money�. When you receive the �free money�, you start to play with it until you either lose all of it or double it at least (makes it 100 units or more). All the 100 units (50 units �free money� wager + 50 units net win) are your own already. You have met the bonus requirements. Of course you can play 50 units "free money" along with 50 units "real money", but it is not a must. And thus the situation become a little bit complicated and risky (you will expose "real money"). But if this is the case, you play with "free money" and "real money" simultaneously, and you win your bet (say without DD or splitting), you receive 200 units (or 250 if you get a BJ). The bonus is completed and you can keep all the 200 (250) units. If you choose to surrender, you lose the 50 units "free money". The bonus is done with. If you decide to double down, you�ll have to put extra 100 units �real money�. This is the case with splitting too. In a case of push, you don�t lose the "free money" and may go on playing with it until you meet the bonus requirements. I hope this clarifies the things. As to the edge precise calculation, thanks to Mr. Schlesinger�s remarks, it will look like this (1 hand taken in account):

Expected Value =-10*0.0024+(100*(1-0.0475)+125*0.0475)* 0.0054*0.45=0.221885625
Player�s edge=0.22/10=0.022=2.2%

It would be very kind if you give me a piece of advice on bankroll requirements taking in account the standard deviations for all the 3 events involved (playing BS, receiving 7-7 and playing with "free money").

Blackjack Rookie

YW nt (nt)

Sim Results

Blackjack Rookie,

I ran two sims. In each, a lone heads up player plays basic strategy, flat-betting $10/round (think of "dollars" as "units").

The first was a 200-million round sim without the bonus, simply to check the house edge and the normal standard deviation.

Albert

Sunday, December 06, 2009, 07:39 PM

---

Summary

Here a summary by seat or player is displayed. Hands skipped indicates hands not played due to "Wonging." Action is Total $ bet per hour and Win Rate is $ won per hour. IBA is advantage related to the Initial Bet (before double downs.) Std. Devs. are always by player and DI is Desirability Index as defined by BJ Attack.

	Hands			$/Hour		Units W/L	Advan.			Std Dev				Performance
Seat	Played	Skip	%	Action	WinRate	Units W/L	TBA%	IBA%	SE	Hand	Hour	100	Shoe	DI	SCORE	N0	Factor
1	205,254,346			$1,116.18	($1.99)	-398,559	-0.179	-0.199	.008	1.11	11.08	11.08	1.1	-1.80	-3.23	-	-.129
2
3
4
5
6
7

Strategies

Seat	Playing Strategy	Betting Strategy
1	6D S17 DA2 DAS ES10 ENHC	Flat Bet
2
3
4
5
6
7

Totals

Rounds: 200,000,000

Hands: 205,254,346

Shoes: 200,000,000

Hours: 2,000,000

Here, we see the house edge is about 0.2%, and the standard deviation is 1.11.

The second sim was a 2-billion-round sim with the bonus included. Note that I has to modify the B.S. to prevent the player from splitting a dealt 7-7, since if he split the software failed to award the bonus... I doubtless failed to set something correctly, but I doubt this small change will appreciably alter the results. Note also that I simply awarded the player 50 units (5 bets) each time he was dealt 7-7, since from your description the "funny money" seems to be almost as good as cash. Here are the new results:

Albert

Sunday, December 06, 2009, 07:46 PM

---

Summary

Here a summary by seat or player is displayed. Hands skipped indicates hands not played due to "Wonging." Action is Total $ bet per hour and Win Rate is $ won per hour. IBA is advantage related to the Initial Bet (before double downs.) Std. Devs. are always by player and DI is Desirability Index as defined by BJ Attack.

	Hands			$/Hour		Units W/L	Advan.			Std Dev				Performance
Seat	Played	Skip	%	Action	WinRate	Units W/L	TBA%	IBA%	SE	Hand	Hour	100	Shoe	DI	SCORE	N0	Factor
1	2,046,269,536			$1,111.72	$25.62	5.1231e7	2.304	2.561	.002	1.10	11.03	11.03	7.3	23.23	539.72	1,853	21.589
2
3
4
5
6
7

Strategies

Seat	Playing Strategy	Betting Strategy
1	ENHC Do not split 7s	Flat Bet
2
3
4
5
6
7

Totals

Rounds: 2.E+9

Hands: 2.046E+9

Shoes: 45,856,564

Hours: 19,999,410

Here, we see the player enjoys a very healthy 2.561% Initial Bet Advantage. In addition, the standard deviation is practically the same as for the non-bonus game, which means that you can use the same bankroll considerations as you would for the non-bonus game.

A few more questions:

1. I assume that on a bet of less than 10 units, you get no bonus, correct?

2. Do you get the bonus for dealt 7-7 ONLY on a 10-unit bet, or on any bet of 10 units or more?

3. If the latter, is the bonus proportional to the bet? For example, if you bet 20 units are are dealt 7-7, do you get 100 units of funny money?

4. Can you save the funny money for another visit if you don't have the chance to play it off on the day you win it?

Dog Hand

A few more answers

Dog Hand,

Thanks again. The sim results are too promising.

As to your questions, the matters stand like this:
1. On a bet of less than 10 units, one gets no bonus;
2. The player gets the bonus of 50 units, on any bet of 10 to 99.99 units;
3. On a bet of 100 units or more, one is entitled to 100 units free money;
4. The player can�t save the funny money for another visit.

Thus, the initial situation (flat-betting 10 units per round) is the most profitable.

Best regards,

Blackjack Rookie