Blackjack Apprenticeship Risk Of Ruin

A podcast about gambling, and life, and their intersection. – Listen to Risk of Ruin instantly on your tablet, phone or browser - no downloads needed. Theoretically, your risk of ruin given infinite hands and finite bankroll should be 100%. As there is a string of games that you can lose in a row that will wipe out your bankroll, and if you play infinite hands, you are guaranteed to play said string. So, I don't understand what people mean by 'risk of ruin' in general. 400 Units: 20% Risk of Ruin. For any of us who've played blackjack professionally, you would never want to run at this level for long, as you wouldn't want to wipe out your capital once out of every 5 bankrolls. But I know Ben and I started higher than this. So again, you can decide if 20% is appropriate relative to your other options.

1. Blackjack Apprenticeship Risk Of Ruin Death
2. Blackjack Apprenticeship Basic Strategy
3. Blackjack Apprenticeship Risk Of Ruin The Following
4. Blackjack Apprenticeship App

Blackjack Betting and Risk of Ruin for the Basic Strategy Player

[Editor's note: Brother William's article about fluctuations in your blackjack bankroll when flat betting and playing basic strategy have a new relevance for players who are taking advantage of online casino bonuses or loss rebate plays. If you are a basic strategy player for any reason, study the article and chart below to get a handle on the normal fluctuations you can expect in your blackjack bankroll. --Arnold Snyder]

In the June 1995 issue of Blackjack Forum, I suggested that it would be helpful to basic strategy blackjack players to print detailed risk charts indicating standard deviation (fluctuation) for flat betting when playing basic strategy. I think there is a danger for players who are milking comps and promotions in not understanding these risks.

In an attempt to remedy this problem, I have created an all-purpose risk chart for the basic strategy player. I hope basic strategy blackjack players will study this chart carefully.

How to Use the Blackjack Basic Strategy Betting Risk Chart

Assumptions:

If you have that kind of bankroll, your risk of ruin is just 1%. On the other hand, if your tolerance for risk is better than that, you could get away with a much smaller bankroll—maybe 200 units. You'd still need $20,000, but you'd be able to play at that level. Your risk of ruin goes way up, though—to 40%.

1. House advantage over the basic strategy player is 0.54% (which would correspond precisely to a 6-deck shoe game with Strip rules, but works pretty well for most games available anywhere, as the house edge is usually set around ½% over the basic strategy player).

2. 60 hands per hour of play. (This is pretty close to what you'll average with a full table.)

3. Flat betting 1 unit per hand.

Regardless of what your unit size is, you may use this chart simply by multiplying. If you were playing $1 per hand, then all of the chart entries in units can simply be read right from the chart in dollars and cents. Example: betting $1 per hand for 16 hours of play, as per the assumed game conditions, you would have an expected loss of $5.18. You will be within one standard deviation (SD) of this expectation 68% of the time, which translates to an actual result between a loss of $39.27 and a win of $28.90. You will be within three standard deviations 99.7% of the time, which translates to an actual result between a loss of $117.80 and a win of $86.69.

Using a $100 betting unit, if you intend to play a total of 16 hours of basic strategy in this game and you're willing to accept a risk level of three SD's, simply move the decimal point two places to the right. You would expect to lose $518.00, but your actual result 99.7% of the time would fall between a loss of $11,780.00 and a win of $8,669.00.

So, if you can stand the thought of losing somewhere around $12,000 every rare once in a while in 16 hours of play, you can afford to flat bet this game with black chips.

The charts are very easy to use with flat bets of $1, $10, $100 and $1000, because you simply have to move the decimal point. For flat bets of $5 or $25 or whatever, just use a pocket calculator.

Note that the entry in the 'expected loss' column can be used to estimate what you are actually 'paying' for any comps your action buys.

Again, I hope any basic strategy blackjack players out there will study this chart carefully. The bankroll you save my be your own. Good luck! ♠

For information on professional gamblers' betting strategies for blackjack, see Arnold Snyder's Blackbelt in Blackjack.

What are the chances of you doubling your blackjack bankroll vs. busting out?

by Henry Tamburin

Do you think the probability of doubling your bankroll would increase or decrease if you decreased your starting bankroll, say, from $200 to $100? Or what if you started with a bigger bankroll? Do you think that would improve your chances of doubling it?

A reader sent me this question about her chances of doubling her bankroll:

I'm a basic strategy player. Let's say I sit down at a $10 minimum table with a $200 bankroll. I say I have a greater than 50% chance of doubling my bankroll before going broke. My husband says I have less than a 50% chance. Can you settle this argument and tell me who's right?

This is an interesting problem and one that mathematicians have actually studied for centuries. A mathematical equation was developed, called the 'Gambler's Ruin,' which allows you to calculate the probability of doubling a bankroll before going broke for a given house edge, bankroll size, and number of betting units. The equation assumes an even-money payoff, which is not always the case in blackjack (due to doubling down, pair splitting, and 3-2 payoffs for a blackjack). However, for many reasonable numbers of units of bank, it gives a close approximation of the probability of doubling a bankroll vs. going broke.

If we assume that the basic strategy player is facing a –0.5% edge, the math says that a basic strategy player has about a 46% probability of doubling a $200 bankroll, playing $10 units. (So your husband wins the argument, but not by much!)

To be clear, this assumes there are no time constraints when you play, meaning you sit down and play until you either win $200 or lose $200. Under these conditions, your chance of doubling your bankroll is 46%, and your chance of busting out is 54%.

Now let me pose this question. Do you think the probability of doubling your bankroll would increase or decrease if you decreased your starting bankroll, say, from $200 to $100? Or what if you started with a bigger bankroll? Do you think that would improve your chances of doubling it?

The answers to questions like these can be found using the 'risk of ruin' calculators on http://www.card-counting.com/blackjack-calculators.htm, which were adapted from the formulas in Don Schlesinger's book Blackjack Attack. The calculator gives these results for different sizes of bankrolls, assuming a negative expectation game:

Blackjack Apprenticeship Risk Of Ruin Death

The percentages in the table clearly show that the chances of a basic strategy player doubling his bankroll (vs. going broke) decrease if he starts with a larger bankroll. This makes sense, because the larger the bankroll that you try to double when you bet one unit on each hand, the longer you will have to play—and the more your bankroll will be exposed to the house edge (thus increasing your chance of going broke before doubling the bankroll).

However, even if the player starts with a relatively small 10-unit bankroll, he still doesn't have a greater than 50% chance of doubling his bankroll—which is logical, given that he is playing a negative expectation game with nearly even-money payoffs.

Now, what if a basic strategy player takes a more conservative approach and instead of trying to double, say, a 20-unit bankroll, he sets a goal to win just 10 units (i.e., he is satisfied with winning 50% of his starting bankroll)? Would he have a greater than 50% chance of achieving his goal? The answer is yes. His chance of winning 10 units with a 20-unit starting bankroll, before tapping out, is 64.12% according to the calculator.

The above examples bring up two important points for basic strategy players who face a negative expectation:

1. You stand the best chance of doubling your bankroll by making a minimum number of large-size bets in relation to the size of your bankroll. (Ideally, the best bet is to wager your entire bankroll on one hand, but few blackjack players would want to play that way.)

1. You have a greater chance of achieving a conservative goal of winning, say, 20–30% of your starting bankroll than you do of trying to double your bankroll.

Finally, what if a basic strategy player is more concerned about getting the maximum amount of playing time with his bankroll—meaning he wants to play a specific number of hours without going broke? For example, suppose a player wants to sit down at a blackjack table with $200, bet $5 a hand (meaning he has 40 units of bank), and play for four hours (i.e., 400 hands). What is the chance that he will tap out before his four-hour playing-time goal?

You can get a quick-and-dirty answer to the above question by going to Appendix 12 (Risk of Ruin) on the blackjack page at www.wizardofodds.com. The appendix has a table that allows you to quickly determine the risk of ruin for different number of hands played and betting units (the table assumes the basic strategy player has a 0.4% negative expectation). In the above example, a player has roughly a 10% chance of losing his $200 bankroll when he bets $5 a hand over four hours (i.e., on average, in one out of 10 four-hour sessions he will lose his $200 bankroll, and in the other nine sessions, his bankroll will last).

Suppose the player increases his bet size from $5 to $10, so he now has only 20 units of bank. Now his risk of ruin increases to 40%, meaning that in four out of 10 four-hour sessions he will lose his $200 bankroll. Therefore, if you are a basic strategy player, and your goal is to get the maximum playing time, you should bet small in relation to your bankroll.

The above information on the chance of doubling your bankroll and the risk of ruin applies to basic strategy players only (i.e., players who face a negative expectation when they play blackjack). If you happen to be a card counter playing with a positive expectation, your chance of doubling your bankroll (and your risk of ruin) is quite different. But that's a story for a future column.

Blackjack Apprenticeship Basic Strategy

Tamburin's Tip of the Month

If I asked you how you would play a 12 against a dealer's 4, you would likely say 'stand.' And this is, in fact, the correct basic strategy play when you don't consider what cards make up your 12. In some games, however, if your 12 happens to be composed of a 10 and a 2, you are slightly better off hitting against a dealer's 4.

However, even if the player starts with a relatively small 10-unit bankroll, he still doesn't have a greater than 50% chance of doubling his bankroll—which is logical, given that he is playing a negative expectation game with nearly even-money payoffs.

Now, what if a basic strategy player takes a more conservative approach and instead of trying to double, say, a 20-unit bankroll, he sets a goal to win just 10 units (i.e., he is satisfied with winning 50% of his starting bankroll)? Would he have a greater than 50% chance of achieving his goal? The answer is yes. His chance of winning 10 units with a 20-unit starting bankroll, before tapping out, is 64.12% according to the calculator.

The above examples bring up two important points for basic strategy players who face a negative expectation:

1. You stand the best chance of doubling your bankroll by making a minimum number of large-size bets in relation to the size of your bankroll. (Ideally, the best bet is to wager your entire bankroll on one hand, but few blackjack players would want to play that way.)

1. You have a greater chance of achieving a conservative goal of winning, say, 20–30% of your starting bankroll than you do of trying to double your bankroll.

Finally, what if a basic strategy player is more concerned about getting the maximum amount of playing time with his bankroll—meaning he wants to play a specific number of hours without going broke? For example, suppose a player wants to sit down at a blackjack table with $200, bet $5 a hand (meaning he has 40 units of bank), and play for four hours (i.e., 400 hands). What is the chance that he will tap out before his four-hour playing-time goal?

You can get a quick-and-dirty answer to the above question by going to Appendix 12 (Risk of Ruin) on the blackjack page at www.wizardofodds.com. The appendix has a table that allows you to quickly determine the risk of ruin for different number of hands played and betting units (the table assumes the basic strategy player has a 0.4% negative expectation). In the above example, a player has roughly a 10% chance of losing his $200 bankroll when he bets $5 a hand over four hours (i.e., on average, in one out of 10 four-hour sessions he will lose his $200 bankroll, and in the other nine sessions, his bankroll will last).

Suppose the player increases his bet size from $5 to $10, so he now has only 20 units of bank. Now his risk of ruin increases to 40%, meaning that in four out of 10 four-hour sessions he will lose his $200 bankroll. Therefore, if you are a basic strategy player, and your goal is to get the maximum playing time, you should bet small in relation to your bankroll.

The above information on the chance of doubling your bankroll and the risk of ruin applies to basic strategy players only (i.e., players who face a negative expectation when they play blackjack). If you happen to be a card counter playing with a positive expectation, your chance of doubling your bankroll (and your risk of ruin) is quite different. But that's a story for a future column.

Blackjack Apprenticeship Basic Strategy

Tamburin's Tip of the Month

If I asked you how you would play a 12 against a dealer's 4, you would likely say 'stand.' And this is, in fact, the correct basic strategy play when you don't consider what cards make up your 12. In some games, however, if your 12 happens to be composed of a 10 and a 2, you are slightly better off hitting against a dealer's 4.

Blackjack Apprenticeship Risk Of Ruin The Following

The reason that hitting becomes a slight favorite over standing when you hold a 10-2 against a 4 is due to the effect of removing the 10 from the deck, which makes it less likely that you will bust when you hit (plus if you stood on 12, with a 10 in your hand, the only way you could win is if the dealer busts, and the likelihood of this occurring decreases when you have a 10 in your hand—which you're wishing was the dealer's hole card). Keep in mind that this is a very close play, more so with a six-deck game compared to a single- or double-deck game. So here is the complete basic playing strategy for 10-2 against a 4.

(Note: s17 means that the dealer must stand on soft 17; h17 means the dealer must hit soft 17).

1. For a single-or double-deck game with either s17 or h17, always hit.
2. For a six-deck game with s17, always hit.
3. For a six-deck game with h17, always stand.
4. For an eight-deck game with either s17 or h17, always stand.

Blackjack Apprenticeship App

Risk Of Ruin – Blackjack.