How Advantage Gamblers Use Risk of Ruin to Improve Their Results

Advantage gamblers hone their skills in a specific game so that they can make long term profits. And the most common advantage play methods/games include card counting, daily fantasy sports (DFS), poker, sports betting, and video poker.

The goal in any of these games is to maximize your profits through a combination of strategy and large bets. Here’s an example:

  • A sports bettor must win 52.4% of the time to break even (w/ 10% house vigorish).
  • You win 54% of your sports bets.
  • You have a 1.6% long term advantage over other bettors.
  • Your average bet size is $1,000.
  • Your average profit per bet is $16.

Winning $16 on a $1k bet certainly isn’t going to make you rich, but a total betting volume of $2 million would yield a $32,000 profit.

Obviously, this sounds great if you want to supplement your income or even make a full time living through gambling.

But advantage players must also think about what happens if luck doesn’t go their way.

After all, the 1% to 3% edge that most pro gamblers have doesn’t guarantee anything. And there’s the possibility that you could lose everything.

This refers to the risk of ruin concept, which is important to any aspiring advantage player. Understanding and applying risk of ruin to your favorite game gives you a better chance of winning in the long run.

That said, I’m going to discuss this concept in detail along with how you can apply it to various advantage play games/methods.

What is Risk of Ruin?

Risk of ruin refers to the likelihood that you’ll lose your entire bankroll. Here’s a simple example:

  • I bet my entire bankroll on a single coin toss.
  • I have a 50% chance of winning.
  • My risk of ruin is 50%.

Both gamblers and investors use risk of ruin to calculate the odds of loving everything, and I’ll briefly discuss how gambling and investment risk of ruin compare to each other later.

In gambling, this concept is often referred to as “gambler’s ruin.” But the idea is the same in that you’re trying to find out the odds of losing everything.

Unfortunately, the average gambler’s ruin situation doesn’t work out as neatly as a coin toss. Instead, you’re left trying to determine the longevity of your bankroll in multi bet situations.

Here’s an example using card counting to illustrate this point:

  • You have a 1.5% advantage (50.75% win rate).
  • Your bankroll is 100 units.
  • You hope to win 100 units before losing 100 units.
  • Your risk of run is 4.72%.

No serious card counter would start with a 100-unit bankroll, but this is an easy way to express the bigger picture.

Here’s one more example to show how your gambler’s ruin rate goes down with more units:

  • You have a 1.5% advantage (50.75% win rate).
  • Your bankroll is 300 units.
  • You hope to win 100 units before losing 300 units.
  • Your risk of run is 0.012%.

Increasing your bankroll to 300 units now makes your risk of ruin much lower.

Players without an advantage are facing a different scenario with gambler’s ruin. They too will lower their risk by having a larger bankroll.

But the key difference is that you’re guaranteed to eventually lose over time. Let’s take the same example from above, only putting you at a disadvantage:

  • You’re facing a 1.5% house edge (49.25% win rate).
  • Your bankroll is 300 units.
  • You hope to win 100 units before losing 300 units.
  • Your risk of run is 95.02%.

Your bankroll is three times larger than your desired profit goal. Nevertheless, you’re still facing elevated risk in this situation.

Why is Understanding Risk of Ruin Important to Advantage Gamblers?

Advantage gamblers want to bet at a level where they can make solid profits without putting their bankroll in jeopardy. Furthermore, they don’t want to risk too much in the short term, because one bad run can ruin them.

It makes little sense to place oversized bets when you have a small long-term advantage. Your goal should be to exploit this small edge over time.

Understanding gambler’s ruin helps you do this by realizing what kind of bankroll you need to avoid busting. This allows advantage players to determine how large their bankroll should be before they start gambling.

Another important point here is how volatile advantage gambling can be.

Some people think that just because somebody has an edge, they’re going to win in almost every session. But this isn’t true at all, especially when dealing with anywhere from a 0.5% to 5% edge.

Even advantage players suffer through ups and downs. Having an adequate bankroll ensures that you survive the low points so that your advantage can be realized.

Obviously, I’d love to play poker heads up with somebody whom I have a 10% advantage over. If I put my entire bankroll into one hand, then my risk of ruin is 40%.

It’s much better to space this matchup out by playing reasonable stakes and having a large bankroll. This way, my 10% edge brings me consistent profits throughout the game.

How do You Calculate Risk of Ruin?

The easiest way to calculate gambler’s ruin is by finding a calculator that make the work easier. I’m using a calculator at BJStrat.net, and you can also find these at QFit.com and GamesBlackjack.org.

These tools are nice because you can input a few variables and calculate your risk of ruin. Here’s an example of what I’m currently entering:

  • Units to risk (bankroll / average bet size) = 200
  • Units profit = 50
  • Win rate = 50.5%
  • Expected value (edge) = 1%
  • Risk of ruin = 1.59%

You need to know your win rate before you get an accurate number out of a gambler’s ruin calculator. And this is easier said than done for advantage situations.

But you should be able to develop a good idea on your win rate with experience. And once you have all of the necessary components, you can use a calculator to quickly figure out gambler’s ruin.

A risk of ruin calculator doesn’t work out so cleanly for every game. For example, poker and card counting call on players to make variable bets based on the situation.

However, any advantage player can still benefit from figuring out their gambler’s ruin.

Applying Risk of Ruin to Different Forms of Advantage Gambling

Card Counting

Some card counters start with as little as a few thousand dollars, but you need a much larger bankroll to avoid a high gambler’s ruin rate.

The minimum you should begin playing with is $20,000 to $25,000. A really safe estimate is anywhere between $40,000 and $50,000.

The challenge in calculating gambler’s ruin for card counters is that you spread your bet during favorable counts. Here’s a common way of spreading bets:

  1. Table minimum is $10 – You bet $10 until the count rises.
  2. Determine a unit size when increasing bets (e.g. $50).
  3. Determine your true count (running count / remaining decks in shoe).
  4. Subtract 1 from true count (e.g. 4 – 1 = 3).
  5. Multiply this number by your unit size (50 x 3 = 150).
  6. You bet $150 during a true count of +3.

The true count doesn’t rise above +3 very often, so most of your bets will be in the $10 to $150 range.

To simplify things, you can make your average bet worth $80 ([10 + 150] /2). You can then use $80 in combination with your bankroll to determine the number of betting units.

But you’ll be making the $10 minimum bet the majority of the time. Plus, there’ll be times where you wager $100 when the true count is +2.

Therefore, you may want a more detailed number to use for determining risk of ruin. Here’s an example of how you can figure this out:

  • 8 deck shoe.
  • You bet $10 for six of the decks (75%).
  • You bet $100 for one deck (12.5%).
  • You bet $150 for one deck (12.5%).
  • Approximately 24 hands per shoe (3 per deck).
  • 24 x 0.75 = 18 hands played at $10 ($180).
  • 24 x 0.125 = 3 hands played at $100 ($300).
  • 24 x 0.125 = 3 hands played at $150 ($450).
  • $930 in total bets / 24 hands = $38.75 average bet.

The next step is to divide your bankroll by the average bet size, then plug this into the risk of ruin calculator. If your bankroll is $38,750, you’d divide this by $38.75 to come up with 1,000 units.

You then use the betting units in the gambler’s ruin calculator like normal. You’ll have little if any risk of ruin when counting cards with this many units.

Daily Fantasy Sports

Daily fantasy sports run in tournament format. This means that you pay a buy in plus a small house fee to compete.

Here’s a sample DFS buy in:

  • $10 + $1 tournament buy in.
  • $10 goes to the prize pool.
  • $1 goes to the site for running the event.

Of course, you must take the entire amount into account for risk of ruin purposes. Speaking of which, you start by determining your average betting unit.

The tricky part here is that you’re probably going to play a variety of buy in levels. But you should be able to come up with a reasonable guess on your average fees based on what stakes you play.

For this example, say that your average buy in is $20 + $2. If your bankroll is worth $2,200, you divide by $22 to get 100 units (buy ins).

You can see a risk of ruin example based on other added variables:

  • 100 betting units
  • Goal = winning 100 units
  • You have a 6% edge (53% win rate)
  • Risk of ruin = 0.001%

As you can see, having 100 units and a 6% edge in DFS tournaments makes it highly unlikely that you’ll lose everything.

Poker

The same DFS gambler’s ruin model covered above can be applied to poker tournaments. After all, this is the same format – just with another game.

Poker cash games are different than tourneys, though, because you’re not dealing with fixed buy ins. Instead, you buy into a cash game (max 100 big blinds) and can win or lose a variable amount.

This means that the tools you use for calculating gambler’s ruin in cash games change. In fact, these tools expect you to use a predetermined risk of ruin to decide your bankroll size.

Professional players are supposed to assume a gambler’s ruin of 1% or lower. Amateurs should use a figure between 1% and 5%.

Here are the variables that you plug into a calculator to determine your bankroll requirements:

  • Big blinds (bb) won per 100 hands.
  • Standard deviation per 100 hands.
  • Risk of ruin (1% to 5%).

ReviewPokerRooms.com has a tool that you can use to calculate these variables, but you have to know your standard deviation before proceeding.

Standard deviation refers to the volatility of your results over 100 bb (or hands). The higher your standard deviation, the more volatile your results will be.

Playing style affects how close your win rate will be to the average. Aggressive players will see a wide variation in their 100 bb results.

The easiest way to find your standard deviation is by using PokerTracker while you play online (when allowed). This software tracks your hands and offers you helpful statistics afterward.

PokerDope.com has a calculator that lets you enter variables and see your poker variance.

You can even calculate variance manually by tracking your results every 100 hands. This data can then be entered into Excel to determine your standard deviation.

Let’s start by assuming your variance is 4 bb per 100 hands. Now that you have this figure, plug everything into ReviewPokerRoom’s calculator.

Here’s an example:

  • Win rate = 2 bb per 100 hands
  • Standard deviation = 4 bb
  • Goal risk of ruin = 2%
  • Bankroll = 15.65 cash buy ins

The calculator also offers the following figures on risk of ruin based on the numbers above:

  • 2.77 buy ins = 50% risk of ruin
  • 5.55 = 25%
  • 9.21 = 10%
  • 11.98 = 5%
  • 15.65 = 2%
  • 18.42 = 1%
  • 21.19 = 0.5%
  • 27.63 = 0.1%
  • 36.84 = 0.01%

A professional player would need at least 18.42 cash buy ins to reach a 1% gambler’s ruin. Your bankroll will be almost untouchable with 27.63 buy ins and a 2-bb win rate.

Sports Betting

Sports wagering is the easiest advantage play activity for determining your risk of ruin. One reason why is because you don’t have to deal with variable bet sizes when using the same unit.

You’re also not dealing with scattered results like with poker cash games and card counting. Instead, you either win or lose your wager.

Many sports bettors like to break their bankroll down into 100 units, then wager one to two units per contest. This simple model keeps your gambler’s ruin low without much thought required.

Plugging variables into a risk of ruin calculator doesn’t actually take a lot of time. Here’s an example:

  • Betting units = 100
  • Goal for units profit = 100
  • Win rate = 54%
  • Expected value = 1.6% (sports bettors break even at 52.4%)
  • Risk of ruin = 3.92%

Sportsbooks take 10% from the losing side, which is why you need to win at least 52.4% of your bets to break even. Your risk of ruin to win 100 units is still fairly high at 3.92%.

This means that you might want to have an even larger bankroll than the standard 100-unit recommendation. Let’s plug in 200 units to see what happens:

  • Betting units = 200
  • Goal for units profit = 100
  • Win rate = 54%
  • Expected value = 1.6% (sports bettors break even at 52.4%)
  • Risk of ruin = 0.16%

Your gambler’s ruin decreases considerably when you add another 100 units to your sports betting bankroll.

Video Poker

Video poker is perhaps the most difficult advantage game with regard to gambler’s ruin. The reason why is because it has multiple payouts that range from one coin up to 4,000 coins.

And you can’t just use a standard gambler’s ruin calculator, because it doesn’t account enough for standard deviation. Nevertheless, you can still figure out what kind of bankroll you need to avoid busting in this game.

The three most common video poker machines that you can make a profit with include:

  1. Full pay Deuces Wild = 100.76% payback
  2. 10/7 Double Bonus = 100.17%
  3. 10/6 Double Bonus = 100.07%

You need to choose one of these games to be an advantage video poker player, and that means you’ll need a calculator that determines risk of ruin for these specific machines.

Video Poker for Winners, which is found at VideoPokerforWinners.com, is one popular tool that can help you. But you’ll have to pay $49.95 for this program, and it only works on PCs.

The Wizard of Odds offers free charts on Deuces Wild and a 10/7 Double Bonus that explain bankroll requirements.

His table factors in cashback (CB) with regard to bankroll requirements. The Wizard also counts the 5-coin max bet ($1.25) as one unit, because this is the only way to reach 100.76% payback.

Here’s one excerpt from the Deuces Wild chart based on 25% cashback:

  • 50% risk of ruin = 771 units (5 coins)
  • 40% = 1,019
  • 30% = 1,339
  • 20% = 1,790
  • 10% = 2,562
  • 7.5% = 2,882
  • 5% = 3,333
  • 2.5% = 4,104
  • 1% = 5,123
  • 0.5% = 5,894
  • 0.25% = 6,665
  • 0.1% = 7,685
  • 0.05% = 8,456
  • 0.025% = 9,227
  • 0.01% = 10,246

Video poker is a fast paced and volatile game. This is why you need so many units to avoid busting while chasing profits.

Risk of Ruin in Gambling vs. Investing

Advantage gambling draws many parallels to investing. And one of these parallels is risk of ruin, because investors also use this concept to determine the odds of losing all of their capital.

But stock and cryptocurrency traders differ from gamblers in that they have different strategies. Specifically, they can hedge investments and diversify.

Hedging refers to mixing your portfolio with safer and riskier investments to mitigate risk. Furthermore, you want the investments to be opposite of each other so that your risk is close to zero.

Here’s an example:

  • You buy stock in Louis Vuitton because they’ve released a popular new item.
  • But you’re also worried that this luxury brand won’t fare well in a rumored recession.
  • You purchase Walmart stock, because this discount retailer does well in recessions.

Experienced investors have more complex ways to hedge, but this represents an easy way of doing it.

Diversification refers to purchasing a broader range of assets to limit your risk. You can diversify with a wide range of stocks, or do it by purchasing stocks, cryptocurrencies, commodities, and bonds.

Certain forms of advantage gambling can also incorporate hedging and diversification.

Sports bettors will sometimes hedge bets in a way that minimizes losses. Poker players can “buy pieces” of other tournament opponents’ buy ins so they have more “horses” in the field.

But outside of these examples, gambling strategy is different from investing. Therefore, you protect yourself from risk of ruin in a different matter.

I believe investing features a smaller risk of ruin when dealing with a comparative bankroll. The reason why is because it’s so easy to diversify in stocks and lower the risk.

Contrast this to video poker, where you need to play the same machine over and over to win.

Conclusion

Gambler’s ruin applies to any game of chance, whether it be slot machines or roulette. Keep in mind that advantage gamblers benefit the most from understanding this concept when compared to the average bettor.

The reason why is because advantage players rely on their bankroll to make consistent profits. And as long as you can protect this bankroll, you have a stronger long-term chance of winning.

The math behind determining risk of ruin is intimidating at first. But luckily, there are calculators and other tools to help in the matter.

One more thing worth mentioning is that the math behind gambler’s ruin gets easier. And once you figure out your risk of ruin for a particular game, you won’t have to continually perform these calculations.

Considering this last thought, I highly recommend that you spend the short amount of time it takes to calculate gambler’s ruin.

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