This is our 4th article on bankroll management. If you haven't read the previous articles in this series, then you should probably do so before continuing with this article. The previous articles discuss the concepts, while this article focuses on the actual bankroll calculations. If you're not familiar with terms like variance, then you should probably read the previous 3 articles first!
- Never Go Broke Playing Poker: learn about poker variance
- MTT Poker Bankroll Management: understand how variance applies to poker tournaments
- 5 Essential Tips to Protect your Poker Bankroll: learn how to reduce the impact of variance
To demonstrate how much your results can deviate from the expected as the number of entries increases, we have calculated the standard deviation of winnings over 1,000 multiplayer poker tournaments for various field sizes, which we have summarized in the tables below. If you play 10 MTTs/day, 6 days a week, it will take you roughly 4 months to complete 1,000 tournaments!
The first thing you need to know is your expected ROI (return on investment), which is shown in the top row of each of the tables below. If you play 1,000 $10 tournaments ($10,000 invested) and have $12,000 in winnings, then you have a 20% ROI ([$12,000 - $10,000] / $10,000). The better you are at tournaments, the higher your ROI will be. Until you've played thousands of tournaments, you won't have a very good estimate of what your expected ROI is. As you will see as we go through the tables, even 1,000 tournaments will not give you a very accurate ROI, especially if you play MTTs with large fields. Keep in mind that an ROI of 20% is very high, and the best tournament players in the world have only around a 30% ROI.
Each table lists the minimum poker bankroll requirements for various expected ROI’s.
|95%||The number of buy-ins required to have a 95% chance to avoid going broke. Use this row to calculate your optimal buy-in if you can afford to replenish your bankroll from a secondary source of income.|
|99.7%||The number of buy-ins required to have a 99.7% chance to avoid going broke. Use this row to calculate your optimal buy-in if you are unable to replenish your bankroll (and thus cannot afford to lose it all).|
The standard deviation listed for each tournament size is the standard deviation of total profit/loss (in terms of buy-ins) after 1,000 tournaments for the samples analyzed for all ROIs. The larger this number is, the more your results may vary from the expected outcome. Your expected earnings (in terms of buy-ins) after 1,000 tournaments is equal to your ROI multiplied by 1,000. That is, if you have a 20% ROI, then after 1,000 tournaments you expect to win 200 buy-ins.
Unfortunately, the distribution of profit/loss after 1,000 tournaments is far from normal, so the empirical rule cannot be applied. That is, 95% of the results will not occur within 2 standard deviations of the average.
|Win Chance||The percentage of the samples that showed a profit after 1,000 tournaments for the given ROI and number of entries. Note that the win rate decreases as the number of entries increases. That is, you can be less assured of actually showing profit even if you are a winning player for each run of 1,000 tournaments. The lower the win rate, the longer it will be before you can be guaranteed to show a profit.|
|Avg. Low ROI||To further highlight the impact of the standard deviation, we have calculated the average profit (or loss) from the worst result from each group of 10 samples of 1,000 tournaments. In other words, there is a greater than 5% chance that your return on investment will be worse than this amount!|
The accuracy of the data decreases as the number of entries increases, so we ran more samples for the larger field tournaments to improve the accuracy of our results.
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Heads-Up Tournament Bankroll Requirements
Based on the fees for a $100 buy-in heads-up PokerStars sit and go. Standard Deviation = 31 buy-ins
|Avg. Low ROI||-1.2%||5.2%||10.6%||15.2%||21.1%||24.7%||31.5%||33.8%|
Okay, so what is this table telling us?
- The 2nd and 3rd rows tell us how big your bankroll should be, depending on whether you can afford to "reload". If you have a full time job that pays your bills, then use the 95% row. If poker is your primary source of income, then you should use the 99.7% row. So, if you're a casual player who plays $10 heads-up SNGs with a 15% ROI, then your bankroll should be $196 (19.6 x $10). If playing $10 heads-up SNGs for a living, then you need to maintain a bankroll of $231 (because otherwise you could go broke). As we can see, the higher your expected ROI, the lower your bankroll requirements are.
- The Win Chance represents the chances of you showing profit after 1,000 tournaments. As you can see, a winning player with a 5% ROI has a 13% chance of being in the red even after 1,000 tournaments! Variance is a bitch!
- The Avg. Low ROI represents a reasonable "worst case scenario". That is, you only have a 5% chance of having a lower ROI than this after 1,000 tournaments. Thus, a player with a 10% expected ROI can reasonably expect to earn at least 52 buy-ins after 1,000 tournaments (5.2% ROI). In other words, even though your expected ROI might be 10%, there's a 5% chance that you could earn as little as 5.2% even after 1,000 tournaments! This is why it's very difficult to estimate your expected ROI. Sure, you may have a 20% ROI now, but you might be massively out-performing your expected results! We can sort of think of the Avg. Low ROI as a "+/-"*. As you can see, your ROI after 1,000 heads-up SNGs is +/-5-6%, regardless of your expected ROI.
*This isn't entirely true. It's fairly accurate for the "-" estimation, but as we move to higher entry tournaments, the "+" will become more stretched. That is, a single lucky win could put you FAR above your expected ROI even after 1,000 tournaments due to the top-heavy nature of tournament prize structures. However, it's still a good indicator of your expected variance.
9-player Sit & Go Tournament Bankroll Requirements
Based on the fees and payout structure for a $10 buy-in 9-player sit & go at Full Tilt Poker, which pays 3 places (33.3%). Standard Deviation = 51 buy-ins
|Avg. Low ROI||-3.7%||3.0%||6.8%||12.9%||17.2%||22.3%||27.3%||32.1%|
Okay, so what do we learn from this table?
- The biggest learning point here is that going from playing heads-up to 9-handed SNGs doubles our bankroll requirements! Playing $10 tournaments with a 15% expected ROI requires a bankroll of $415 ($494 if we can't reload).
- We also start to see increased variance:
- Even players with a 10% expected ROI aren't guaranteed to be ahead after 1,000 tournaments
- As many as 5% of these players will earn as little as 3% ROI despite a 10% expected ROI (down from 5% for heads-up SNGs). That is, the "+/-" for your ROI after 1,000 tournaments has increased to 7% (from 5% for heads-up SNGs).
45-player Sit & Go Tournament Bankroll Requirements
Based on the fees & payout structure for a $1 buy-in 45-player sit & go at PokerStars, which pays 7 places (15.6%). Standard Deviation = 93 buy-ins
|Avg. Low ROI||-8.1%||-3.1%||2.0%||7.4%||11.4%||14.0%||21.1%||26.5%|
Going from 9-player to 45-player tournaments, we learn that:
- Our bankroll requirements double once again! Playing $10 tournaments with a 15% expected ROI requires a bankroll of $1,070 ($1,300 if we can't reload).
- Variance is becoming more of an issue:
- Even players with a 20% expected ROI aren't guaranteed to show profit after 1,000 tournaments
- 5% of players with a 10% expected ROI will be in the red after 1,000 tournaments!
- The "+/-" of your actual ROI vs expected after 1,000 tournaments has increased to 13% (and keep in mind that this is the +/- range for 95% of the players; 5% will experience even greater highs or lows).
90-player Sit & Go Tournament Bankroll Requirements
Based on the fees and payout structure for a $2.50 buy-in 90-player sit & go at PokerStars, which pays 13 places (14.4%). Standard Deviation = 115 buy-ins
|Avg. Low ROI||-11.5%||-5.7%||-0.9%||3.5%||7.2%||13.0%||15.3%||18.4%|
As we can see, the trend continues: the more entries there are, the higher our variance becomes. Even top tournament players with a 25% expected ROI aren't guaranteed to show profit after 1,000 tournaments! This is one of the big advantages of Sit & Go tournaments over MTTs: reduced variance! If you want to play poker professionally, a steady income should be a top priority, and this is far easier to achieve from SNGs. If reduced variance is your top concern, then we highly recommend you download and install PokerStars, especially if you plan to play multiple SNGs simultaneously. No other site offers as many SNGs as PokerStars.
However, professional online poker players also understand the benefits of playing SNGs, which is why SNGs tend to be tougher than MTTs. So if you're going to grind Sit & Go tournaments, you should probably invest in some poker training, such as the Sit & Go Booster from Ace Poker Solutions. At just $24.95, this complete poker course will quickly pay for itself!
As mentioned above, MTTs tend to attract weaker players. There are two reasons for this:
- Large prize pools tend to attract gamblers, and gamblers tend to be bad poker players.
- It's far easier for a bad MTT player to fool themselves into thinking they are just unlucky. If you are deep in the red after 1,000 MTTs, you can always blame variance. But if you are deep in the red after 1,000 9-handed SNGs, then you are a losing player. Most people would rather believe the lie than face the truth! As a result, bad MTT players tend to stick around longer, whereas it becomes apparent much sooner if you are a bad SNG player.
So if MTTs are more profitable in the long run, we need to figure out a way to benefit from the increased ROI without decimating our bankrolls. And the solution to this is to play primarily smaller field tournaments!
122-player Tournament Bankroll Requirements
Based on the fees and payout structure for a $5.50 buy-in tournament at PokerStars with 122 entries that pays 13 places (10.7%). Standard Deviation = 116 buy-ins.
|Avg. Low ROI||-11.6%||-6.8%||-2.3%||2.6%||7.3%||13.9%||18.9%||25.2%|
As we can see, even with just 122 entries (a fairly small MTT), even top tournament players with a 25% expected ROI are not guaranteed to show profit after 1,000 tournaments. And playing a $10 tournament of this size requires a bankroll of $1,000 to $2,000.
Let's use this information in a practical example. Let's assume you're a better MTT player (20% ROI) than single table SNG player (15% ROI). You have a bankroll of $1,200, and plan to play some MTTs with an average of 122 entries. You play poker casually, so you're willing to accept a 5% chance of going broke. The table above tells us that you need 121 buy-ins for your bankroll. This means you should be playing $9.90 tournaments ($1,200 / 121 = $9.92). After 1,000 tournaments, you expect to earn $1,980 (20% x $9.90 x 1,000 = $1,980), but there's a 5% chance you could earn as little as $257.40 (2.6% x $9.90 x 1,000 = $257.40).
Okay, but what if you played 9-handed SNGs, where you only have a 15% expected ROI? Well, you would only need a bankroll of 41.5 buy-ins, meaning you could play $25 tournaments ($1,200 / 41.5 = $28.92). Let's assume that your expected ROI drops by another 5% playing higher stakes. With a 10% expected ROI, you'd need a bankroll of 52.0 buy-ins, meaning you could play $22 tournaments ($1,200 / 52.0 = $23.1). After 1,000 tournaments, you expect to earn $2,200 (10% x $22 x 1,000 = $2,200). So, even though your expected ROI is HALF, you are able to earn slightly more simply because the reduced variance means you can risk more per tournament! And it gets even better, because your "worst case" is $680 (3.0% x $22 x 1,000 = $680), which is more than DOUBLE your minimum expected from larger field tournaments. Plus, 9-handed SNGs take far less time to complete, so with the same amount of time invested, you could probably complete double or triple the number of tournaments, which means double or triple the profits!
243-player Tournament Bankroll Requirements
Based on the fees and payout structure for a $16.50 buy-in tournament at PokerStars with 243 entries that pays 32 places (13.2%). Standard Deviation = 160 buy-ins
|Avg. Low ROI||-16.8%||-10.5%||-7.3%||-2.2%||-0.1%||7.7%||10.8%||15.3%|
These are still considered "small" MTTs, and yet after 1,000 tournaments, there's a 5% chance that even incredibly skilled tournament poker players won't show profit. If you're playing 10 MTTs/day, 6 days a week, that's a potential 4-month period without profit! For tournaments of this size, you should only be risking around 0.5% of your bankroll. That means that if you want to play a $10 MTT with 243 players, then you should have a bankroll of $2,000. The vast majority of poker players are not disciplined enough to invest just 0.5% of their bankroll in a single tournament, which is why so many poker players go broke!
549-player Tournament Bankroll Requirements
Based on the fees and payout structure for a $5.50 buy-in tournament at PokerStars with 549 entries that pays 72 places (13.1%). Standard Deviation = 216 buy-ins
|Avg. Low ROI||-22.8%||-18.7%||-15.4%||-10.1%||-7.9%||-2.5%||0%||5.4%|
We are now starting to get into the bigger tournaments, where a single $10 investment could net you $800 to $900 in profit. However, as the table shows, the variance is becoming a real problem! After 1,000 tournaments, a player with an expected ROI of 20% ($2,000) has a 5% chance of being $1,000 in the red! So how do we balance our desire for a big payday with our need to play within the means of our bankroll? There are three options:
- Risk a smaller portion of your bankroll in large field events. That is, if you have a $2,000 bankroll and a 15% expected ROI, then you should be playing $15 tournaments with roughly 100-150 entries ($2,000 / 128 buy-in bankroll requirement = $15.62). But if playing tournaments with 500-750 entries, you should only be playing $5 events ($2,000 / 301 buy-in bankroll requirement = $6.64). You will still have massive variance in your results, but by strictly adhering to our bankroll calculations, you can minimize the risk of going broke!
- Play the vast majority of your tournaments (90+%) as smaller field events (<250 entries). For example, if you're playing 10 MTTs/day, then start the day with a single large field event, and then play smaller field events for the rest of the day. This way you're still getting a shot at a big payday, but also mitigating the impact that single tournament has on your overall variance.
- Combine the first two options. Many top tournament players have a higher ROI in larger field events. This is because they are very good at adjusting their play for the various stages (building a large stack during the early stages, then aggressively growing it while others are just hanging on to make the money, and continuing to play aggressively in an effort to win, rather than just trying to move up a pay grade). In order to play as many large field events as possible, these players can do a combination of the two solutions above. For example, you could play 50% of your daily MTTs as large field events, but risking slightly less. So, with a $2,000 bankroll, these players might play 50% of their daily MTTs as $15 events with <200 entries, and the the other 50% as $10 MTTs with 500-750 entries. This allows these players to benefit from the larger expected ROI from the bigger events, while also reducing their overall variance with more regular cashes in the smaller ones.
1,215-player Tournament Bankroll Requirements
Based on the fees and payout structure for a $5.50 buy-in tournament at PokerStars with 1,215 entries that pays 180 places (14.8%). Standard Deviation = 286 buy-ins
|Avg. Low ROI||-30.7%||-27.7%||-24.5%||-16.3%||-14.7%||-12.2%||-6.1%||-4.3%|
We are now in typical PokerStars MTT territory. A $22 MTT on PokerStars will frequently see these sorts of entries. If you want to regularly play $22 MTTs on PokerStars, then your bankroll should be at least $7,000, and that's if your expected ROI is 15%! Expect massive swings in your bankroll if regularly playing tournaments with over 1,000 entries. This is one of the reasons we so strongly promote Americas Cardroom. Not only do they offer better rewards plus lower rake/fees than every other online poker site, but their tournaments also tend to be big enough, without being too big (typically 100-200 entries).
2,570-player Tournament Bankroll Requirements
Based on the fees and payout structure for The Big $16.50 at PokerStars with 2,570 entries that pays 324 places (12.6%). Standard Deviation = 394 buy-ins
|Avg. Low ROI||-42.2%||-36.4%||-35.3%||-32.2%||-27.6%||-20.3%||-18.2%||-13.4%|
Not only do larger fields reduce the percentage of your poker bankroll you can invest per tournament, but they also increase the number of tournaments you must play to guarantee you will show profit!
You may wish to add an additional 20% to our calculations for non-heads-up tournaments since the maximum downswings will not result in a normal distribution (making the empirical rule less accurate). However, if you have the discipline to drop down in buy-ins if your bankroll dwindles, you can also cut the required number of buy-ins in half. This will allow you to invest more of your poker bankroll per tournament, but will still give you the required number of buy-ins to protect yourself against going broke. Note that you MUST be disciplined for this approach to work. It’s awfully tempting to continue playing at a higher buy-in in an attempt to dig oneself out of a hole. However, this road leads to poker poverty!
One of the best ways to reduce your bankroll requirement is to increase your expected ROI, AKA "git gud". The best way to improve your tournament ROI is by investing in quality poker tournament courses. You can also check out this awesome review of the Raise Your Edge Tournament Masterclass. Alternatively, you may want to consider hiring a poker coach from this list of the best poker coaches.
Up to this point we have only been discussing bankroll requirements for tournaments. Calculating bankroll requirements for cash game poker is significantly more complicated because cash games have many more variables. Unlike with tournaments, there are no pre-determined payouts or set number of players. We have always planned to add an additional two articles to this series, but until then, I highly recommend this article on bankroll management as it discusses cash games in much more detail, and includes plenty of tips for managing your cash game bankroll.