Some blackjack players are so preoccupied with mastering perfect basic strategy and card counting that they neglect their money management. In blackjack, just like in any other casino-banked game, managing one’s bankroll adequately is of great significance.

Risk of Ruin and Drawdown Calculator Just fill in the stats of the trading system, the test length and the level of drawdown/ruin to be tested and hit the Calculate button. Click on “How to interpret the results” for more information. This calculator is a variation of the return & variance calculator. It includes all the functions of the standard calc, along with an hours of play estimate. Only blackjack is supported at this time. The player speed input and software selection pulldown are used to estimate your rate of play.

Having said that, we would also like to point out bankroll management is powerless when it comes to decreasing the house edge. What it does help with is longevity, or preserving your blackjack bankroll for a longer period of time. No matter how perfect your play is, you are guaranteed to lose your money without discipline and proper bankroll management.

Building a Bankroll – How Much Money Do You Need to Play Blackjack?

Let’s start by specifying that your bankroll is the money you have set aside strictly for the purpose of playing blackjack. We suspect you already know this but just to play it safe, we shall say it again – you should never use money you need to cover your day-to-day expenses for playing blackjack, regardless of your level of skill or previous experience.

Our advice is to place your blackjack bankroll in a separate account and withdraw from it when you plan to attack the blackjack tables. Once you finish with the assault, you go back and deposit whatever you have left alongside any winnings you have generated during the session.

You should leave your bankroll alone in the beginning and avoid using it for any non-blackjack-related purchases. Once you succeed in building your bankroll, you can reward yourself by buying something with some of the winnings you have generated.

Table Limits and Session Bankrolls

With this clarification out of the way, we warn you there is no uniform bankroll size that applies to absolutely all blackjack players. The edge skilled players get inevitably manifests itself over the long term. Anything can happen over the course of a single session, a week, or even a few months.

Experiencing short-term losses, even if you are an accurate card counter, is hardly anything unheard of. The bottom line is as a serious blackjack player, you need a bankroll that is large enough to withstand the losses you may incur on a short timescale.

The overall amount you allocate for blackjack play should be broken down into smaller session bankrolls. How much you allocate for a single session is closely linked to what table limits you play.

If there are lots of casinos in your area but you have limited funds for blackjack play at your disposal, the smartest thing to do is scout the different gambling halls and find a table with low enough limits to accommodate your small bankroll. Provided that there is a single casino with high limits in your city, you better wait until you save a sufficiently large bankroll to play such stakes.

Show MoreHide MoreA session bankroll should be at least 50 times the lowest bet at the table. This is the bare minimum, recommended for basic strategy players and flat bettors. Respectively, players who count cards and move their bets with the true count are recommended to put aside at least 100 times their top bets.

Thus, if there are $10 tables in your vicinity and you flat bet at this minimum with basic strategy, your session’s bankroll should be at least $500. Your max bet should not exceed the amount of $10 under any circumstances. Provided that you are a novice card counter who uses a less aggressive bet spread like 1 to 5, you will need a session bankroll of at least $5,000.

Each number 1 through 5 corresponds to the number of base bets you need to wager when you move with the true count. You put out 5 units or $50 on a count of +5 or higher, 4 units or $40 on a count of +4, and so on. One unit of $10 is wagered on a count of +1 as well as on neutral and negative counts.

Evaluating Your Risk of Ruin

Disciplined players who exercise good money management are well-acquainted with the term “Risk of Ruin”, abbreviated as RoR. For those of you who are not, RoR denotes the probability of a given player losing their entire bankroll.

There are several values you need to take into account when estimating your Risk of Ruin, including your standard deviation, your bankroll in units, and your win rate per every hundred hands. There are free RoR calculators on the web players can use to accurately estimate the likelihood of busting their full bankrolls. Your other option is to use blackjack simulators that can calculate the RoR for you.

We can distinguish between two types of Risk of Ruin, namely session RoR and the RoR for players’ full bankroll. The former denotes the likelihood of the player losing their entire bankroll for the session while the latter shows you the probability of busting your overall lifetime bankroll.

To give you an example, let’s suppose you have a session bankroll of $2,000, play perfect basic strategy, and flat bet $10 per hand. You have 200 base betting units at your disposal. The software you are using has calculated that you have a session RoR of 18%.

This means that eventually you will end up losing your $2,000 around 18% of the time. And the opposite, your bankroll will increase 82% of the time. Meanwhile, if you cut your bankroll in half to $1,000, or 100 units, your RoR will jump to nearly 32%, which exceeds the tolerable limits. In the other 68% of the time, you will increase the bankroll.

It is important to specify that different players are willing to put up with different RoR percentages. At the end of the day, this is all a matter of individual tolerance. The bottom line is the bigger your bankroll is and the more base betting units you have, the lower your RoR will be.

Understanding Standard Deviation

The term standard deviation (SD) is normally used in mathematical statistics in relation to the distribution of expected results. In blackjack, it denotes the distribution of players’ results within a range of probable outcomes.

It tells you how frequently a specific outcome will deviate from your expected average. This is important because it enables you to assess whether you are playing a losing or a winning game as well as to decide how big your bankroll should be for any given session.

It is unrealistic to think you can win each and every blackjack session, even if you are perfect at basic strategy and count cards with great accuracy. A low standard deviation indicates the actual results fall closely within one’s expectations.

We shall explain how standard deviation works with a simple coin-flipping example. A coin has a 50% chance of landing on tails and a 50% chance of landing on heads. Yet, you cannot expect the coin to land precisely 50 times on tails and 50 times on heads in every 100 trials, or at least not in the short term. Sometimes it may land only 45 times on tails and 55 times on heads which happens roughly 2/3 of the time or around 68.3%.

Show MoreHide MoreIn the context of blackjack, the standard deviation of a single hand you play in a six-deck game is estimated at 1.14. Thus, you are expected to win or lose roughly 1.14 bet units around 68.3% of the time within one standard deviation, 2.28 betting units will be lost/won 95% of the time within two standard deviations and 3.42 units will be lost/won 99.7% of the time within three standard deviations. The distribution of these results is shown on the so-called Gaussian bell-curves.

Knowing their standard deviation enables players to calculate the probability of winning or losing a given number of units over the course of a certain number of hands. You do this by multiplying your standard deviation by the square root of the number of hands you play.

So if your sample size involves 400 hands with a standard deviation of 1.14, you can expect to lose or win √400 x 1.14 = 20 x 1.14 = 22.8 betting units around 68.3% of the time. Respectively, 95% of the time, you can expect results within two standard deviations where you will lose √400 x 2.28 = 20 x 2.28 = 45.6 betting units over the course of 400 hands. And finally within three standard deviations, you will lose √400 x 3.42 = 20 x 3.42 = 68.4 betting units every 400 hands 99.7% of the time.

Standard deviation may be complex to understand if you are a novice but is nevertheless of great importance. You need it when calculating your RoR, which in turn helps you determine the bankroll you need. Do not be intimidated, however, as you can figure out what your RoR is by using a simulator software or one of the online RoR calculators.

House Edge and Hourly Losses

The beauty of using basic strategy is that it reduces the house edge in blackjack to such an extent that you are nearly playing a break-even game. Yet, basic strategy is not powerful enough to completely overcome the built-in casino advantage.

Even if you are perfect at basic strategy, the house edge will inevitably cause a dent in your blackjack bankroll over the long run. This dent, however, will be far more significant if you rely on gut feelings and hunches instead of using the optimal strategy.

Knowing the house edge of a blackjack game helps you calculate the hourly losses you can expect to incur in the long term. Suppose you choose a table with more liberal rules like those offered across Las Vegas Strip casinos where the house edge revolves around 0.36%.

You multiply this percentage by the average number of hands you play per hour and your average bet size. Assuming you are a recreational player who joins mostly full tables and bets $30 per hand on average, you will be able to go through roughly 80 hands per hour.

Therefore, the long-term hourly losses you can expect to see will amount to ($30 x 80 hands x 0.36)/100 = 864/100 = $8.64.You will inevitably arrive at this figure when you get enough playing hours under your belt. By “enough”, we mean tens of thousands of hours as anything can happen in the short run.

Unlike basic strategy players who are practically betting on a negative EV game, skilled and disciplined card counters are able to overcome the house edge. They have an advantage of around 1% at six-deck games with decent rules.

This enables them to grow their bankrolls overtime instead of incurring long-term losses. They calculate their expected hourly winnings with the same formula, i.e. by multiplying their edge by the average bet size and the number of hands they play per hour.

Respectively, an accurate counter who plays heads-up at an empty table with at a 1% advantage and goes through 100 bets of $30 per hour can expect long-term hourly returns of ($30 x 100 hands x 1)/100 = 3,000 / 100 = $30.

Handling Losing Sessions

Variance is inherent to all casino games, including blackjack. All players, no matter how skilled they are, will inevitably end up going through some losing sessions. Knowing how to handle these and when to call it quits is of great significance for preserving your bankroll.

Needless to say, chasing your losses is a terrible idea. The rule of thumb all smart blackjack players should follow is to always leave a table before they have busted their entire session bankroll. The general recommendation is to throw in the towel when you are left with fewer than six betting units.

Blackjack Bankroll Size

So if you bet $50 per hand, you must ensure you have at least $300 before you continue playing; if you wager $100, you end the session when you are down to less than $600 and so on.

The reason for this is simple – you need enough money to back up any potential splitting and doubling decisions in line with basic strategy. The bottom line is you should never stay at the table if you are so underbanked that you can no longer exercise the optimal playing decisions. Doing the opposite will ultimately cost you money in the long run.

• Appendices
• Miscellaneous
• External Links

Introduction

There are some sources that address the question of the probability of doubling a bankroll before losing it, in a card counting situation. Ken Uston's Million Dollar Blackjack, to name one. This appendix shall not recover that issue. However, I am often asked about how much the basic strategy player's bankroll should be, given a targeted number of hands to play. This is especially practical if the player must play a certain number of hands to earn an online casino bonus.

The rules assumed for these tables are six decks, dealer stands on soft 17, player may double on any two cards, player may double after splitting, player may resplit to three hands, no surrender, dealer peeks for blackjack. Under these rules, the house edge is 0.4140%.

Let's look at an example of how this table can be used. Assume that the player makes a deposit of $1000 to an online casino, and is required to bet through $5000 in action. If the player is to willing to play through 500 hands, then his average bet size would be $5000/500 = $10. The number of betting units would be $1000/$10 = 100. The table shows the risk of ruin is 0.01% for 102 units, so would be just over 0.01% for 100. Perhaps this is too conservative, so the player considers playing 200 hands. The bet size is now $5000/200 = $25. The number of units is $1000/$25 = 40. Interpolating the table shows the risk of ruin would be 1.5%.

Number of Hands to Play

Risk of Ruin	100	200	300	400	500	600	700	800	900
50%	7	11	14	16	18	20	22	24	25
40%	9	14	17	20	23	25	27	29	31
30%	12	17	21	25	28	31	33	36	38
20%	15	21	26	31	34	38	41	44	47
10%	19	27	34	39	44	48	53	57	60
5%	22	32	40	46	52	58	62	67	71
4%	23	34	42	49	55	60	65	70	75
3%	25	36	44	51	58	64	69	74	79
2%	27	38	47	55	62	68	74	79	84
1%	29	42	52	61	68	75	82	88	93
0.5%	32	46	57	66	74	82	89	95	101
0.25%	35	50	61	71	80	88	96	102	109
0.1%	38	54	67	77	87	95	104	111	118
0.01%	45	64	79	91	102	112	122	131	139

Number of Hands to Play

Risk of Ruin	1000	1200	1400	1600	1800	2000	2500	3000
50%	27	30	32	35	37	40	45	50
40%	33	37	40	43	46	49	56	62
30%	41	45	49	53	56	60	68	75
20%	50	55	60	65	69	73	83	92
10%	64	70	76	82	88	93	105	116
5%	76	83	90	97	104	110	124	137
4%	79	87	95	102	108	114	129	143
3%	83	92	100	107	114	121	136	151
2%	89	98	107	114	122	129	145	161
1%	99	108	118	126	134	142	160	177
0.5%	107	118	128	137	146	154	174	192
0.25%	115	126	137	147	156	166	187	206
0.1%	125	138	149	160	170	180	202	223
0.01%	148	162	175	188	198	212	236	261

Methodology

The tables above were created by random simulation. I have been asked several times for a general formula for other situations. Unfortunately there isn't any that I know of. Risk of ruin problems are mathematically usually very complicated. It is easier and more convincing to run a random simulation instead.

Blackjack Bankroll Calculator

Written by: Michael Shackleford