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.
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 40% ROI, then after 1,000 tournaments you expect to win 400 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 | 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 results 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.
Heads-Up Tournament Bankroll Requirements
Standard Deviation = 31 buy-ins
| ROI > | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% |
| 95% (buy-ins) |
45.9 | 26.7 | 19.6 | 16.5 | 13.5 | 12.7 | 10.6 | 9.5 |
| 99.7% (buy-ins) |
55.9 | 31.6 | 23.1 | 19.4 | 15.7 | 14.8 | 12.3 | 11.0 |
| Win Chance | 87% | 100% | 100% | 100% | 100% | 100% | 100% | 100% |
| Avg. Low (buy-ins) |
-12 | 52 | 106 | 152 | 211 | 247 | 315 | 338 |
Based on the fees for a $100 buy-in heads-up PokerStars sit and go.
9-player Sit & Go Tournament Bankroll Requirements
Standard Deviation = 51 buy-ins
| ROI > | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% |
| 95% (buy-ins) | 74.1 | 52.0 | 41.5 | 34.1 | 29.0 | 23.8 | 21.1 | 20.3 |
| 99.7% (buy-ins) | 90.6 | 63.2 | 49.4 | 40.2 | 34.0 | 27.5 | 24.5 | 23.7 |
| Win Chance | 82% | 98% | 100% | 100% | 100% | 100% | 100% | 100% |
| Avg. Low (buy-ins) | -37 | 30 | 68 | 129 | 172 | 223 | 273 | 321 |
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%).
45-player Sit & Go Tournament Bankroll Requirements
Standard Deviation = 93 buy-ins
| ROI > | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% |
| 95% (buy-ins) | 157 | 120 | 107 | 91.2 | 80.3 | 68.9 | 66.7 | 58.1 |
| 99.7% (buy-ins) | 193 | 146 | 130 | 110 | 96.0 | 81.6 | 80.7 | 68.8 |
| Win Chance | 72% | 86% | 96% | 99% | 100% | 100% | 100% | 100% |
| Avg. Low (buy-ins) |
-81 | -31 | 20 | 74 | 114 | 140 | 211 | 265 |
Based on the fees & payout structure for a $1 buy-in 45-player sit & go at PokerStars, which pays 7 places (15.6%).
90-player Sit & Go Tournament Bankroll Requirements
Standard Deviation = 115 buy-ins
| ROI > | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% |
| 95% (buy-ins) | 173 | 170 | 134 | 119 | 109 | 103 | 91.4 | 86.3 |
| 99.7% (buy-ins) |
210 | 206 | 160 | 144 | 130 | 124 | 109 | 103 |
| Win Chance | 71% | 82% | 92% | 97% | 99% | 100% | 100% | 100% |
| Avg. Low (buy-ins) |
-115 | -57 | -9 | 35 | 72 | 130 | 153 | 184 |
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%).
122-player Tournament Bankroll Requirements
Standard Deviation = 116 buy-ins
| ROI > | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% |
| 95% (buy-ins) |
181 | 154 | 128 | 121 | 98.5 | 89.9 | 77.8 | 67.2 |
| 99.7% (buy-ins) | 220 | 188 | 156 | 147 | 118 | 109 | 91.9 | 78.7 |
| Win Chance | 61% | 78% | 89% | 98% | 99% | 100% | 100% | 100% |
| Avg. Low (buy-ins) |
-116 | -68 | -23 | 26 | 73 | 139 | 189 | 252 |
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%).
243-player Tournament Bankroll Requirements
Standard Deviation = 160 buy-ins
| ROI > | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% |
| 95% (buy-ins) |
253 | 238 | 195 | 184 | 161 | 154 | 141 | 126 |
| 99.7% (buy-ins) |
310 | 289 | 235 | 225 | 195 | 186 | 170 | 151 |
| Win Chance | 63% | 76% | 84% | 90% | 94% | 98% | 99.4% | 99.8% |
| Avg. Low (buy-ins) |
-168 | -105 | -73 | -22 | -1 | 77 | 108 | 153 |
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%).
549-player Tournament Bankroll Requirements
Standard Deviation = 216 buy-ins
| ROI > | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% |
| 95% (buy-ins) |
353 | 312 | 301 | 258 | 233 | 219 | 198 | 188 |
| 99.7% (buy-ins) |
435 | 380 | 370 | 311 | 282 | 265 | 240 | 227 |
| Win Chance | 57% | 69% | 75% | 83% | 86% | 92% | 93% | 97% |
| Avg. Low (buy-ins) |
-228 | -187 | -154 | -101 | -79 | -25 | 0 | 54 |
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%).
1,215-player Tournament Bankroll Requirements
Standard Deviation = 286 buy-ins
| ROI > | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% |
| 95% (buy-ins) |
429 | 392 | 363 | 326 | 312 | 289 | 253 | 238 |
| 99.7% (buy-ins) |
519 | 477 | 441 | 397 | 379 | 353 | 305 | 287 |
| Win Chance | 54% | 61% | 66% | 75% | 81% | 84% | 89% | 92% |
| Avg. Low (buy-ins) |
-307 | -277 | -245 | -163 | -147 | -122 | -61 | -43 |
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%).
2,570-player Tournament Bankroll Requirements
Standard Deviation = 394 buy-ins
| ROI > | 5% | 10% | 15% | 20% | 25% | 30% | 35% | 40% |
| 95% (buy-ins) |
513 | 485 | 444 | 413 | 401 | 374 | 347 | 325 |
| 99.7% (buy-ins) |
618 | 584 | 537 | 498 | 490 | 456 | 423 | 395 |
| Win Chance | 51% | 55% | 57% | 65% | 72% | 75% | 78% | 83% |
| Avg. Low (buy-ins) |
-422 | -364 | -353 | -322 | -276 | -203 | -182 | -134 |
Based on the fees and payout structure for The Big $16.50 at PokerStars with 2,570 entries that pays 324 places (12.6%).
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!
Given that winning players typically win by finishing higher in the money than average, most winning players will earn higher ROI as the number of entries increases (since larger field tournaments also have a greater disparity in prize pool distribution). However, your increases in ROI need to offset the increased number of buy-ins required to avoid going broke. For example, if you can earn 10% ROI playing 9-player SNGs, then you would need to earn almost 20% ROI playing 45-player SNGs due to the increased minimum bankroll size (which would decrease your buy-in amount).
9-player sit & go with a 10% ROI with a 95% chance to avoid going broke:
10% x 1,000 tournaments x $1,000/52.0 buy-ins = $1,923
45-player sit & go with a 15% ROI:
20% x 1,000 tournaments x $1,000/91.2 buy-ins = $2,193
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.
Did you find our tables useful? Are there other tables you would like us to add? Let us know your thoughts in the comments section below!
Despite winning the WSOP Main Event in 1980 and then again in 1981, by 1997 Stu Ungar
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