Poker Tournament Formula Spreadsheet

This post works with 5-card Poker hands drawn from a standard deck of 52 cards. The discussion is mostly mathematical, using the Poker hands to illustrate counting techniques and calculation of probabilities

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2. Poker Tournament Formula Spreadsheet Template
3. Poker Tournament Formula Spreadsheet Online
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5. Poker Tournament Formula Spreadsheet Examples

Working with poker hands is an excellent way to illustrate the counting techniques covered previously in this blog – multiplication principle, permutation and combination (also covered here). There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. three of a kind) is the number of possible hands for that type over 2,598,960. Thus this is primarily a counting exercise.

Poker Tournament Formula Spreadsheet Download

Neau's Tournament Formula. One of the most popular poker league points systems is Dr. Neau's Tournament Formula. Neau's Tournament Formula topic in the HPT Forums for more information about this poker league points system that takes into account the number of participants in the tournament, the buy-in cost, the individual player's total expense (buy-ins + add-ons + rebuys.

• Obviously, there are many other topics which you should master, such as poker bankroll management, GTO poker strategy, poker tells, big blind play and many more. Obviously, you have to learn poker in the right way as well and only then you will take full advantage of understanding poker math and implementing poker odds to gain the best possible.
• To ensure that play money has real monetary value, the software will track the financial movements over the course of the game and output an excel spreadsheet that tracks everyone's gains and losses for the night. For a tournament-style game, PokerStars Home Game lets you designate a members-only private poker club. Once you've downloaded the.
• Duncan Palamourdas explains how the three standard methods of deal-making in poker tournaments are calculated: equal chop, chip chop, and ICM chop. 2020 WSOP Main Event.

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Preliminary Calculation

Usually the order in which the cards are dealt is not important (except in the case of stud poker). Thus the following three examples point to the same poker hand. The only difference is the order in which the cards are dealt.

These are the same hand. Order is not important.

The number of possible 5-card poker hands would then be the same as the number of 5-element subsets of 52 objects. The following is the total number of 5-card poker hands drawn from a standard deck of 52 cards.

The notation is called the binomial coefficient and is pronounced “n choose r”, which is identical to the number of -element subsets of a set with objects. Other notations for are , and . Many calculators have a function for . Of course the calculation can also be done by definition by first calculating factorials.

Thus the probability of obtaining a specific hand (say, 2, 6, 10, K, A, all diamond) would be 1 in 2,598,960. If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of all diamond cards? It is

This is definitely a very rare event (less than 0.05% chance of happening). The numerator 1,287 is the number of hands consisting of all diamond cards, which is obtained by the following calculation.

The reasoning for the above calculation is that to draw a 5-card hand consisting of all diamond, we are drawing 5 cards from the 13 diamond cards and drawing zero cards from the other 39 cards. Since (there is only one way to draw nothing), is the number of hands with all diamonds.

If 5 cards are randomly drawn, what is the probability of getting a 5-card hand consisting of cards in one suit? The probability of getting all 5 cards in another suit (say heart) would also be 1287/2598960. So we have the following derivation.

Thus getting a hand with all cards in one suit is 4 times more likely than getting one with all diamond, but is still a rare event (with about a 0.2% chance of happening). Some of the higher ranked poker hands are in one suit but with additional strict requirements. They will be further discussed below.

Poker Tournament Formula Spreadsheet Template

Another example. What is the probability of obtaining a hand that has 3 diamonds and 2 hearts? The answer is 22308/2598960 = 0.008583433. The number of “3 diamond, 2 heart” hands is calculated as follows:

One theme that emerges is that the multiplication principle is behind the numerator of a poker hand probability. For example, we can think of the process to get a 5-card hand with 3 diamonds and 2 hearts in three steps. The first is to draw 3 cards from the 13 diamond cards, the second is to draw 2 cards from the 13 heart cards, and the third is to draw zero from the remaining 26 cards. The third step can be omitted since the number of ways of choosing zero is 1. In any case, the number of possible ways to carry out that 2-step (or 3-step) process is to multiply all the possibilities together.

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The Poker Hands

Here’s a ranking chart of the Poker hands.

The chart lists the rankings with an example for each ranking. The examples are a good reminder of the definitions. The highest ranking of them all is the royal flush, which consists of 5 consecutive cards in one suit with the highest card being Ace. There is only one such hand in each suit. Thus the chance for getting a royal flush is 4 in 2,598,960.

Royal flush is a specific example of a straight flush, which consists of 5 consecutive cards in one suit. There are 10 such hands in one suit. So there are 40 hands for straight flush in total. A flush is a hand with 5 cards in the same suit but not in consecutive order (or not in sequence). Thus the requirement for flush is considerably more relaxed than a straight flush. A straight is like a straight flush in that the 5 cards are in sequence but the 5 cards in a straight are not of the same suit. For a more in depth discussion on Poker hands, see the Wikipedia entry on Poker hands.

The counting for some of these hands is done in the next section. The definition of the hands can be inferred from the above chart. For the sake of completeness, the following table lists out the definition.

Definitions of Poker Hands

Poker Tournament Formula Spreadsheet Online

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Counting Poker Hands

Straight Flush
Counting from A-K-Q-J-10, K-Q-J-10-9, Q-J-10-9-8, …, 6-5-4-3-2 to 5-4-3-2-A, there are 10 hands that are in sequence in a given suit. So there are 40 straight flush hands all together.

Four of a Kind
There is only one way to have a four of a kind for a given rank. The fifth card can be any one of the remaining 48 cards. Thus there are 48 possibilities of a four of a kind in one rank. Thus there are 13 x 48 = 624 many four of a kind in total.

Full House
Let’s fix two ranks, say 2 and 8. How many ways can we have three of 2 and two of 8? We are choosing 3 cards out of the four 2’s and choosing 2 cards out of the four 8’s. That would be = 4 x 6 = 24. But the two ranks can be other ranks too. How many ways can we pick two ranks out of 13? That would be 13 x 12 = 156. So the total number of possibilities for Full House is

Note that the multiplication principle is at work here. When we pick two ranks, the number of ways is 13 x 12 = 156. Why did we not use = 78?

Flush
There are = 1,287 possible hands with all cards in the same suit. Recall that there are only 10 straight flush on a given suit. Thus of all the 5-card hands with all cards in a given suit, there are 1,287-10 = 1,277 hands that are not straight flush. Thus the total number of flush hands is 4 x 1277 = 5,108.

Straight
There are 10 five-consecutive sequences in 13 cards (as shown in the explanation for straight flush in this section). In each such sequence, there are 4 choices for each card (one for each suit). Thus the number of 5-card hands with 5 cards in sequence is . Then we need to subtract the number of straight flushes (40) from this number. Thus the number of straight is 10240 – 10 = 10,200.

Three of a Kind
There are 13 ranks (from A, K, …, to 2). We choose one of them to have 3 cards in that rank and two other ranks to have one card in each of those ranks. The following derivation reflects all the choosing in this process.

Two Pair and One Pair
These two are left as exercises.

High Card
The count is the complement that makes up 2,598,960.

The following table gives the counts of all the poker hands. The probability is the fraction of the 2,598,960 hands that meet the requirement of the type of hands in question. Note that royal flush is not listed. This is because it is included in the count for straight flush. Royal flush is omitted so that he counts add up to 2,598,960.

Probabilities of Poker Hands

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2017 – Dan Ma

Poker Tournament Strategy: The Differences between Harrington on Hold'em and Snyder's Poker Tournament Formula

A Difference in the Primary Focus of the Strategies

A number of players and commentators seem confused about the differences between the poker tournament strategy presented in Harrington on Hold 'em, and the poker tournament strategy presented by Arnold Snyder in The Poker Tournament Formula

Specifically, commentators like Mason Malmuth of 2+2 Publishing and Steve Zolotow of Card Player have been confused by one particular superficial similarity between the strategies—the fact that both strategies advocate looser starting hand requirements as your chip stack grows smaller. Because of this superficial similarity, Malmuth and Zolotow have called Snyder's strategy a weak imitation of Harrington's. Nothing could be further from the truth.

Actually, the specific starting hand requirements advocated by Harrington and Snyder are vastly different, and so is the criterion by which they judge the adequacy of stack size and determine how much to loosen up. But these are not the most important differences between the two strategies. Arnold Snyder is writing a separate article that will address the differences in starting hand requirements and the significance of these differences. In this article, I will address the deeper, fundamental differences between the Snyder and Harrington strategies.

Harrington's strategy is a conservative, or tight, strategy. The decision to play is almost always initiated by the cards you receive: You wait for the best hand you are likely to receive, mathematically, within a given amount of time. Harrington advocates bluffing, including blind steals, only once every hour and a half. With such infrequent bluffing in the Harrington strategy, poker skill comes into play chiefly in how you play your cards.
Snyder emphasizes the importance of tournament factors other than cards in making decisions both on whether to enter pots and how to play hands. In fact, Snyder specifically states in The Poker Tournament Formula that cards are the least important weapon at your disposal in poker tournaments, no matter how well you play those cards.

In The Poker Tournament Formula, Snyder emphasizes the importance of chips and position over cards in a winning poker tournament strategy. Chips and position are the keys to player manipulation, and the whole Poker Tournament Formula strategy is built around player psychology and player manipulation for the purpose of much more frequent bluffs.
To oversimplify a key difference, the Harrington strategy is focused on cards, while the Snyder strategy is focused on theft.

Current M versus Tournament Structure

And there are other important disagreements between the Harrington and Snyder strategies that sharpen the light on this difference in focus. For example, Harrington emphasizes current M (the size of your stack relative to the costs of a round) in making tournament hand selection decisions. He doesn't consider overall structure (future M, or acceleration of M) except when you're within a few minutes of entering the next blind level.
Snyder emphasizes the importance of overall tournament structure, rather than current stack relative to the costs of a round, in determining whether to enter a pot and how to play any hand. Basically, Snyder's idea is that by the time you're forced to play according to M, you're in bad shape in a tournament.

In focusing on M, Harrington is focused on survival, on giving himself the best possible chance of hitting 'good cards.' He is focused on calculating the cost of a round because he wants to know how long he can go without playing a hand before he gets short or blinded-off. When you are not short in chips, Harrington advocates patience.

Snyder, who thinks cards are the least important weapon in a tournament, is focused on chips and the psychological and strategic power of a big stack. He advocates emphasizing earning with skills related to chips and position long before tournament structure starts to limit opportunities to earn with skill. For more information on the importance of a chip lead in Snyder's strategy, see Snyder's article Reverse Chip Value Theory: Good Math, Bad Logic (A Reply to David Sklansky), particularly the article's discussion of 'Chip Utility Value.'
One of the chief disadvantages of the Harrington style is that you get short more often, which means a Harrington player will be forced into low-skill all-in confrontations too often in tournaments. Some players seem to believe that the style advocated by Snyder will get you busted out early more often, and that's true to an extent, but these players greatly overstate both the frequency of this occurrence and the frequency with which Harrington's waiting style will pay off.
Harrington understands, and specifically states (in Harrington on Hold 'em II) the value of maintaining enough chips to play a poker hand after the flop. Again, he is focused on cards, and on playing his cards with skill. While Harrington does briefly address the importance of average stack size, he does very little with it in determining overall tournament strategy.

All decisions about what cards to play are based on your current stack relative to the costs of a round (or the costs of a round in the next 15 minutes), and decisions about how to play those hands are based primarily on your current M and the M of opponents, with only a glance at current average stack size, and no consideration of tournament structure.
Snyder understands the value of chips in playing a hand with skill (again, see Snyder's chip utility discussion), but his book focuses on the more overarching value of a chip lead in terms of overall tournament strategy. To Snyder, a chip lead both maximizes your gains from manipulating your opponents, and sets a player up for the luck portion of a tournament.

Unlike Harrington, Snyder looks at the overall structure of a tournament to determine when the luck portion of a tournament will start and how many chips a player needs to have earned by that point. Snyder correctly points out that the tournament effectively ends at that point, which may be hours before the final table, and that being short at this point is the mathematical equivalent of losing.

The Most Important Difference: Why Snyder's Poker Tournament Strategy Inevitably Beats Harrington's Over the Long Run

In closing, it is a fact of professional gambling that those who can get their money in action with an edge more frequently will earn more than those whose strategies identify profitable betting opportunities less frequently.

And the biggest difference between Snyder's Poker Tournament Formula strategy and Harrington's strategy is that Snyder's strategy will identify profitable betting opportunities more frequently than Harrington's strategy will. Therefore, Snyder's strategy is superior to Harrington's. Let me say that again, to make it absolutely plain: You will make more money in tournaments with Snyder's strategy than you will with Harrington's strategy.

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Poker Tournament Formula Spreadsheet Examples

It should be noted that the basic strategy presented in The Poker Tournament Formula is geared for tournaments of a particular speed (meaning a specific blind structure relative to starting chips). Specifically, Snyder's basic strategy and specific hand-play recommendations were designed for tournaments of a speed he calls Skill Level 3.

Snyder is the first author to present an easy method of identifying which fast tournaments offer significant advantages for skillful players, and which don't. Authors like Steve Zolotow claim that fast tournaments are unbeatable, and I have no doubt whatsoever that Zolotow has not been able to beat them, but it's not because fast tournaments are truly unbeatable. Players like Zolotow lose at fast tournaments partly because they are failing to identify which fast tournaments can be beaten, and partly because they are using the wrong strategies for the tournaments, out of the mistaken belief that tournament structure doesn't matter.

In any case, since tournament structure is crucial to optimal poker tournament strategy, Snyder's specific 'basic strategy' (hand-playing tactics and other details) for Skill Level 3 tournaments will have to be adjusted by players for tournaments of different speeds. But the underlying principles of the strategy in The Poker Tournament Formula, with starting hand selections and hand-playing tactics adjusted for tournament structure, will beat Harrington's strategies in any tournament, fast or slow. ♠

[Note: Again, there are numerous other specific differences between the Harrington and Snyder strategies that are important enough that Arnold Snyder will be discussing them in a separate article.

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