This assumes that all bets made are of equal size. The probability that the session outcome will be within one standard deviation is 68.26%. The probability that the session outcome will be within two standard deviations is 95.46%. The probability that the session outcome will be within three standard deviations is 99.74%. Variance in Fixed Limit Holdem. Both of these examples will behave according to picture above. The picture shows how many data will fit in interval from the center line. +- 1Sigma it is about 70% of all occurences - bus from previous example will arrive by 70% in interval 4 minutes 40s to 5 minuts and 20 seconds.
In this article we'll first address how to calculate your win rate for both cash games and tournaments. Then we'll consider a few ways you might use that information to improve your game going forward, including talking about both the positives and the pitfalls that can potentially come with a knowledge of your win rate. Finally, we'll address the question everyone seems to have when it comes to this topic — 'What is a good win rate?'
Calculating Your Win Rate in Cash Games
One note before we start — 'win rate' obviously refers to the rate at which a player is winning. Of course, if the rate is being calculated for a losing player, the number will be negative, which might make it seem misleading to call it a 'win rate,' but that is the term that continues to be used regardless.
If you are a no-limit hold'em cash game player, you will typically calculate your win rate in one of two ways — either by hour or by 100 hands. With each method you also have an option to figure your win rate according to cash won or according to the number of big blinds won.
Live players often calculate win rates per hour, since it can be distracting to count the number of hands they have played while at the table. For example, a player who plays a six-hour session and comes away with a $120 profit has enjoyed a $20/hour win rate for that day.
Online players can more easily keep track of the number of hands they have played, as many sites provide easy-to-consult running totals. Online poker analysis programs like Hold'em Manager and PokerTracker also help players find such information, along with a host of other statistics regarding their play. Also, many online players tend to multi-table, which depending on how many tables they have open could wildly affect the number of hands they play per hour. Therefore, calculating win rates per 100 hands often makes more sense as a standard when playing online.
Say an online player plays a 600-hand session and wins $60. That player's win rate could be described as $10/100 hands. However, those who play online NLHE cash games typically prefer to speak of their win rates in terms of big blinds won per 100 hands — or BB/100.
Let's say that online player won $60 playing 600 hands of $0.50/$1.00 no-limit hold'em. The big blind in the game is $1, meaning the player ultimately profited by 60 BBs. That's a win rate of 60 / 600 = 10 BB/100.
Calculating Your Win Rate in Tournaments
For tournaments (including sit-n-gos), win rates are typically calculated a little differently than in cash games. Instead of talking about an amount won per hour or number of hands, tournament players — both live and online — often measure their rate of success according to their return on investment or 'ROI.'
Put simply, your ROI is calculated by dividing your overall profits in tournaments (your 'return') by the amount you've spent on tournament buy-ins (your 'investment'). Often the result is then multiplied by 100 and expressed as percentage, thus..
- (winnings - buy-ins) / buy-ins * 100 = ROI%
Imagine you're an online player and a fan of the $3.30 buy-in tournaments on PokerStars. Over the course of a couple of weeks you play 100 of them, with all of your cashes adding up to $370. You've spent $330 on buy-ins, so your profit has been $40. Divide $40 (profit) by $330 (buy-ins) to get 0.12, then multiply that by 100 to get 12% ROI.
Like with win rates in cash games, your ROI will be negative if you spend more on buy-ins than you collect in cashes (i.e., you're a losing player over the period being considered). For instance, if you've won $280 in those 100 tournaments that cost $330 total, your ROI will be around -15%.
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Calculating Your Win Rate: Positives
- Helps you focus on the long term
Online betting sites for casino. Even the best poker players endure bad sessions and downswings. However, having an awareness of your win rate over longer periods can go a long way toward helping you endure the mental stress of losing in poker.
Poker is a game in which skill generally wins out over the long term, but luck can have an disproportionate impact on the short term, especially in tournaments. Keeping accurate records can help you see in an instant how a single bad day or even a lengthy slide doesn't necessarily affect your win rate too greatly over longer periods.
- Helps with game selection
Standard Deviation Of Return
Keeping track of your win rates at various stakes in cash games and your ROI in various tournaments types and buy-ins can help highlight for you which games are your most profitable (and perhaps should be playing more), and also which represent games in which you lose consistently (and perhaps should be playing less or avoiding).
Knowing that you have a solid, positive ROI in that $3.30 buy-in tournament (for instance) and that you're losing consistently in the $5.50 and $11 tournaments you also keep entering might mean you should stop pouring your bankroll into those higher buy-in tournaments. The same goes for cash games, where an understanding of which stakes are best for your win rate can help you know where you should be playing most of your hands.
- Helps with bankroll management
Wheel of fortune pc game free download. Knowing your win rate also can help you make other decisions regarding your bankroll and how much of it you can reasonably risk in a session or tournament. No deposit usa online slots. See 'An Introduction to Bankroll Management' for more on this subject, including how bankroll management directly dictates game selection (or at least it should).
Calculating Your Win Rate: Pitfalls
- Hurts when you look at too small of a sample size
Just as knowing your win rate over the longer term can help you avoid reacting too emotionally over short-term losses, it's also easy to become overly affected by calculations of win rates over very small sample sizes. That player above who is enjoying a handsome 12% ROI over 100 tournaments might be feeling pretty good, but in truth even 100 tournaments isn't really a large enough sample size to suggest that win rate will be sustainable going forward.
Online pros offer differing advice regarding what constitutes a meaningful sample size, though most will tell you anything under 10,000 cash game hands isn't enough to draw meaningful conclusions about win rates. In fact, some argue you need at least 100,000 hands to get a better idea of what your results mean. Such numbers can seem arbitrarily chosen, and you'll find a lot differing viewpoints about them. But the larger lesson here is not to be overly affected by win rates calculated over a clearly small sample size.
- Hurts when you fail to account for different stakes/buy-ins
Go back to that player who won $60 playing 600 hands (a small sample, by the way) of $0.25/$0.50 NLH — a (big) 10 BB/100 win rate. Suppose that player was actually multi-tabling and playing a variety of different stakes games during those 600 hands — say some $0.05/$0.10 hands, a bunch of $0.10/$0.25 hands, and only a few at $0.25/$0.50. The player could still average 10 BB/100 over the 600 hands, but come away a big loser cash-wise if the best BB/100 came at the lowest limits, and the worst BB/100 at the highest.
With cash games, it is often recommended to distinguish between stakes when looking at win rates — that's how you can discover which stakes are most profitable for you, as well as help you make decisions about moving up (or down) limits. It's helpful as well to look at your ROI% in tournaments according to specific buy-ins, although when it comes to tournaments a compiled percentage that includes all of the different buy-ins can still be a useful measure. That's because there often isn't as huge a difference in skill level between players at different tournament buy-ins as there is between cash game players at different stakes.
- Hurts when you falsify your results
Win rates can be dangerous to players who aren't honest with themselves or their record-keeping. They make it easy to isolate a certain period of play and make claims — to others, or to oneself — about having enjoyed a high win rate over the selected period. There's a certain category of players who will even purposely neglect to record losing sessions, practicing a form of denial that extends even to their own, personal poker ledgers.
Keeping records of your play can be immensely helpful as you try to improve as a player, but don't fall prey to being selective and/or inaccurate about your record-keeping in order to rationalize or explain away poor results (even if it's just to yourself).
What Is a Good Win Rate?
This is a very difficult question to answer, deserving of an entire article (or series of articles) on its own.
The Meaning Of Standard Deviations
In cash games, the best players at the lowest stakes are often able to sustain especially high win rates (in terms of BB/100) — much higher than the best players at higher stakes, in fact. Speaking of online players, some estimate that the best no-limit hold'em players at the very lowest stakes are able to win 20-40 BB/100 hands over significantly large sample sizes, with the best players at the higher NLH stakes able to win from 3-8 BB/100 (with those figures affected by how many tables they play at once).
Meanwhile in tournaments anything above 0% ROI is obviously good (marking you as a winning player), while achieving even just 5-10% ROI would place you ahead of the vast majority of players. Going higher than that (20-30% and above) is extremely good, with only the top pros genuinely able to maintain such a clip over the long term.
But on a certain level, judgments about what constitutes a 'good win rate' are always going to be subjective. A good win rate for you will be one that (1) keeps you in the game, and (2) helps you achieve whatever goals you set for yourself as a player. Being able to match or better whatever win rate you've achieved in the past can be a good goal for which to strive, but don't let that introduce unwanted stressors or make the game less enjoyable for you.
Also in this series..
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Introduction
The following table shows the house edge of most casino games. For games partially of skill perfect play is assumed. See below the table for a definition of the house edge.
Casino Game House Edge
| Game | Bet/Rules | House Edge | Standard Deviation |
|---|---|---|---|
| Baccarat | Banker | 1.06% | 0.93 |
| Player | 1.24% | 0.95 | |
| Tie | 14.36% | 2.64 | |
| Big Six | $1 | 11.11% | 0.99 |
| $2 | 16.67% | 1.34 | |
| $5 | 22.22% | 2.02 | |
| $10 | 18.52% | 2.88 | |
| $20 | 22.22% | 3.97 | |
| Joker/Logo | 24.07% | 5.35 | |
| Bonus Six | No insurance | 10.42% | 5.79 |
| With insurance | 23.83% | 6.51 | |
| Blackjacka | Liberal Vegas rules | 0.28% | 1.15 |
| Caribbean Stud Poker | 5.22% | 2.24 | |
| Casino War | Go to war on ties | 2.88% | 1.05 |
| Surrender on ties | 3.70% | 0.94 | |
| Bet on tie | 18.65% | 8.32 | |
| Catch a Wave | 0.50% | d | |
| Craps | Pass/Come | 1.41% | 1.00 |
| Don't pass/don't come | 1.36% | 0.99 | |
| Odds — 4 or 10 | 0.00% | 1.41 | |
| Odds — 5 or 9 | 0.00% | 1.22 | |
| Odds — 6 or 8 | 0.00% | 1.10 | |
| Field (2:1 on 12) | 5.56% | 1.08 | |
| Field (3:1 on 12) | 2.78% | 1.14 | |
| Any craps | 11.11% | 2.51 | |
| Big 6,8 | 9.09% | 1.00 | |
| Hard 4,10 | 11.11% | 2.51 | |
| Hard 6,8 | 9.09% | 2.87 | |
| Place 6,8 | 1.52% | 1.08 | |
| Place 5,9 | 4.00% | 1.18 | |
| Place 4,10 | 6.67% | 1.32 | |
| Place (to lose) 4,10 | 3.03% | 0.69 | |
| 2, 12, & all hard hops | 13.89% | 5.09 | |
| 3, 11, & all easy hops | 11.11% | 3.66 | |
| Any seven | 16.67% | 1.86 | |
| Double Down Stud | 2.67% | 2.97 | |
| Heads Up Hold 'Em | Blind pay table #1 (500-50-10-8-5) | 2.36% | 4.56 |
| Keno | 25%-29% | 1.30-46.04 | |
| Let it Ride | 3.51% | 5.17 | |
| Pai Gowc | 1.50% | 0.75 | |
| Pai Gow Pokerc | 1.46% | 0.75 | |
| Pick ’em Poker | 0% - 10% | 3.87 | |
| Red Dog | Six decks | 2.80% | 1.60 |
| Roulette | Single Zero | 2.70% | e |
| Double Zero | 5.26% | e | |
| Sic-Bo | 2.78%-33.33% | e | |
| Slot Machines | 2%-15%f | 8.74g | |
| Spanish 21 | Dealer hits soft 17 | 0.76% | d |
| Dealer stands on soft 17 | 0.40% | d | |
| Super Fun 21 | 0.94% | d | |
| Three Card Poker | Pairplus | 7.28% | 2.85 |
| Ante & play | 3.37% | 1.64 | |
| Video Poker | Jacks or Better (Full Pay) | 0.46% | 4.42 |
| Wild Hold ’em Fold ’em | 6.86% | d |
Notes
| a | Liberal Vegas Strip rules: Dealer stands on soft 17, player may double on any two cards, player may double after splitting, resplit aces, late surrender. |
| b | Las Vegas single deck rules are dealer hits on soft 17, player may double on any two cards, player may not double after splitting, one card to split aces, no surrender. |
| c | Assuming player plays the house way, playing one on one against dealer, and half of bets made are as banker. |
| d | Yet to be determined. |
| e | Standard deviation depends on bet made. |
| f | Slot machine range is based on available returns from a major manufacturer |
| g | Slot machine standard deviation based on just one machine. While this can vary, the standard deviation on slot machines are very high. |
House Edge
The house edge is defined as the ratio of the average loss to the initial bet. The house edge is not the ratio of money lost to total money wagered. In some games the beginning wager is not necessarily the ending wager. For example in blackjack, let it ride, and Caribbean stud poker, the player may increase their bet when the odds favor doing so. In these cases the additional money wagered is not figured into the denominator for the purpose of determining the house edge, thus increasing the measure of risk.
The reason that the house edge is relative to the original wager, not the average wager, is that it makes it easier for the player to estimate how much they will lose. For example if a player knows the house edge in blackjack is 0.6% he can assume that for every $10 wager original wager he makes he will lose 6 cents on the average. Most players are not going to know how much their average wager will be in games like blackjack relative to the original wager, thus any statistic based on the average wager would be difficult to apply to real life questions.
The conventional definition can be helpful for players determine how much it will cost them to play, given the information they already know. However the statistic is very biased as a measure of risk. In Caribbean stud poker, for example, the house edge is 5.22%, which is close to that of double zero roulette at 5.26%. However the ratio of average money lost to average money wagered in Caribbean stud is only 2.56%. The player only looking at the house edge may be indifferent between roulette and Caribbean stud poker, based only the house edge. If one wants to compare one game against another I believe it is better to look at the ratio of money lost to money wagered, which would show Caribbean stud poker to be a much better gamble than roulette.
Standard Deviation Of A Rate
Many other sources do not count ties in the house edge calculation, especially for the Don’t Pass bet in craps and the banker and player bets in baccarat. The rationale is that if a bet isn’t resolved then it should be ignored. I personally opt to include ties although I respect the other definition.
Element of Risk
For purposes of comparing one game to another I would like to propose a different measurement of risk, which I call the 'element of risk.' This measurement is defined as the average loss divided by total money bet. For bets in which the initial bet is always the final bet there would be no difference between this statistic and the house edge. Bets in which there is a difference are listed below.
Element of Risk
| Game | Bet | House Edge | Element of Risk |
|---|---|---|---|
| Blackjack | Atlantic City rules | 0.43% | 0.38% |
| Bonus 6 | No insurance | 10.42% | 5.41% |
| Bonus 6 | With insurance | 23.83% | 6.42% |
| Caribbean Stud Poker | 5.22% | 2.56% | |
| Casino War | Go to war on ties | 2.88% | 2.68% |
| Heads Up Hold 'Em | Pay Table #1 (500-50-10-8-5) | 2.36% | 0.64% |
| Double Down Stud | 2.67% | 2.13% | |
| Let it Ride | 3.51% | 2.85% | |
| Spanish 21 | Dealer hits soft 17 | 0.76% | 0.65% |
| Spanish 21 | Dealer stands on soft 17 | 0.40% | 0.30% |
| Three Card Poker | Ante & play | 3.37% | 2.01% |
| Wild Hold ’em Fold ’em | 6.86% | 3.23% |
Standard Deviation
The standard deviation is a measure of how volatile your bankroll will be playing a given game. This statistic is commonly used to calculate the probability that the end result of a session of a defined number of bets will be within certain bounds.
The standard deviation of the final result over n bets is the product of the standard deviation for one bet (see table) and the square root of the number of initial bets made in the session. This assumes that all bets made are of equal size. The probability that the session outcome will be within one standard deviation is 68.26%. The probability that the session outcome will be within two standard deviations is 95.46%. The probability that the session outcome will be within three standard deviations is 99.74%. The following table shows the probability that a session outcome will come within various numbers of standard deviations.
I realize that this explanation may not make much sense to someone who is not well versed in the basics of statistics. If this is the case I would recommend enriching yourself with a good introductory statistics book.
Standard Deviation
| Number | Probability |
|---|---|
| 0.25 | 0.1974 |
| 0.50 | 0.3830 |
| 0.75 | 0.5468 |
| 1.00 | 0.6826 |
| 1.25 | 0.7888 |
| 1.50 | 0.8664 |
| 1.75 | 0.9198 |
| 2.00 | 0.9546 |
| 2.25 | 0.9756 |
| 2.50 | 0.9876 |
| 2.75 | 0.9940 |
| 3.00 | 0.9974 |
| 3.25 | 0.9988 |
| 3.50 | 0.9996 |
| 3.75 | 0.9998 |
Hold
Although I do not mention hold percentages on my site the term is worth defining because it comes up a lot. The hold percentage is the ratio of chips the casino keeps to the total chips sold. This is generally measured over an entire shift. For example if blackjack table x takes in $1000 in the drop box and of the $1000 in chips sold the table keeps $300 of them (players walked away with the other $700) then the game's hold is 30%. If every player loses their entire purchase of chips then the hold will be 100%. It is possible for the hold to exceed 100% if players carry to the table chips purchased at another table. A mathematician alone can not determine the hold because it depends on how long the player will sit at the table and the same money circulates back and forth. There is a lot of confusion between the house edge and hold, especially among casino personnel.
Hands per Hour, House Edge for Comp Purposes
The following table shows the average hands per hour and the house edge for comp purposes various games. The house edge figures are higher than those above, because the above figures assume optimal strategy, and those below reflect player errors and average type of bet made. This table was given to me anonymously by an executive with a major Strip casino and is used for rating players.
Hands per Hour and Average House Edge
| Games | Hands/Hour | House Edge |
|---|---|---|
| Baccarat | 72 | 1.2% |
| Blackjack | 70 | 0.75% |
| Big Six | 10 | 15.53% |
| Craps | 48 | 1.58% |
| Car. Stud | 50 | 1.46% |
| Let It Ride | 52 | 2.4% |
| Mini-Baccarat | 72 | 1.2% |
| Midi-Baccarat | 72 | 1.2% |
| Pai Gow | 30 | 1.65% |
| Pai Pow Poker | 34 | 1.96% |
| Roulette | 38 | 5.26% |
| Single 0 Roulette | 35 | 2.59% |
| Casino War | 65 | 2.87% |
| Spanish 21 | 75 | 2.2% |
| Sic Bo | 45 | 8% |
| 3 Way Action | 70 | 2.2% |
Translation
A Spanish translation of this page is available at www.eldropbox.com.
Written by: Michael Shackleford