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David Sklansky explains
Expected Value early in this book.
Sklansky uses a coin flip as an example,
"if someone stupidly offered you $300to$200 of a flip of a coin,
you have an expected value of positive $50." [16]
A key concept with tournaments is that it may not always be right to make the play with higher expected value, "it turns out that in a tournament it is not always right to choose the play with the slightly higher EV. This is because the higher EV bet may be more likely to lose." [17] Slowplaying in tournaments can be dangerous, "Unless you have a 'monster' hand, slowplaying, while often making you more when it works, entails an extra risk of losing the pot. This risk is often worth taking in a regular game, but not in a tournament." [21] The Gap Concept is discussed early in the book, "There is a very important general principle understood by all good poker players. That is, you need a better hand to play against someone who has already opened the betting than you would need to open yourself." [27] The size of the gap depends on how your opponents are playing, "If your opponents are quite loose, there may be no gap at all." [2728] The gap concept is consistent with tournament strategy, "You avoid confrontations with those who have already shown strength, and you take advantage of those who are trying to preserve their chips." [28] The author clarifies that the gap concept does not apply when someone just limps in ahead of you instead of raising before you act. He goes on to say that limping is generally not a good idea in tournaments, "In general, you should rarely limp in in a limit hold'em tournament. There is simply too great a chance that you will steal the blinds with a raise." [51] Strategies change with chip counts, "I have often heard it said that, if your stack is short, you must take chances now because you will not have enough chips to play with once the stakes go up. That is totally wrong. In fact, if anything, the reverse is true." [57] There appears to be a typo on page 65. The author is talking about Q5s in the body but Q7 in the footnote. [65] Allin situations are frequent in tournaments and the author runs through some scenarios. "Suppose you are playing limit hold'em and are in the big blind, and all you have left is just enough to call a raise. All fold to the small blind, who raises without looking at his cards. you have 32. Should you call? Yes because a treydeuce has a 32 percent chance of beating two random cards, and you are getting 3to1 on this call." The footnote explains that "treydeuce is the worst possible hand played against two random cards 'hot and cold', i.e. no betting." [69] It is important to understand how many different ways hands can be dealt, "a pair of aces can be dealt in six different ways, Ditto for the kings. Aceking, on the other hand, can be dealt in 16 different ways." [72] The author makes it clear that one should not raise in no limit hold'em unless the reaction from a reraise is obvious, "So again, do not raise in no limit hold'em, especially tournaments, if there is a reasonable chance that a reraise will make you throw up." [92] AK is a solid hand in nolimit hold'em and it is often best played by moving all in, "moving in before the flop with aceking is often the best way to play that hand. It is important to understand, however, that it is a lot better to be the bettor when you put your money in, rather than calling someone else's allin bet." [116] The author has a system for beginner no limit tournament players. He taught it to a female player as follows: 1. If someone else has raised in front of you, move in all your chips with aces, kings, or aceking suited. Otherwise fold. 2. If not one else has raised in front of you, move in all your chips with any pair, any aceother suited, aceking(suited or offsuit), or two suited connected cards, except for fourtrey or treydeuce. [123] He goes on to elaborate, "Notice that the hands that she was to move in with(again, when no one raised in front of her) comprised about 13 percent of all the two card cominations.(If you don't know how I got that, stop reading this book right now. You are not ready for it. You don't know enough about poker. And, you deserve to lose.)" [124] I thought it would be fun to do the math behind the above statement so I worked it out as follows: Since there are 52 cards and 2 places that means there are combin(52,2) possible hands. In other words there are 52!/50!*2! or 1326 possible hands It is even easier to show with 5 cards in the deck. Suppose the only cards we have are T,J,Q,K,A of clubs. The possible hands are as follows: TJ,TQ,TK,TA, JQ,JK,JA, QK,QA, KA This is equal to 4+3+2+1 or (4+1)*(4/2)=5*2=10 Moving on, we have 51+50+49+...+1=52*51/2=51*26=1326 The hands we move in with are as follows: pairs=13 pairs*6 ways of having each pair=78 aceking=16 two suited connectors except fourtrey and treydeuce means we have: 45s,56s,67s,78s,89s,9Ts,TJs,JQs,QKs(A2s is dealt with in aceother suited)=9*4=36 aceother suited means we have: A2s,A3s,A4s,A5s,A6s,A7s,A8s,A9s,ATs,AJs,AQs=11*4=44 Adding this together we have (78+16+36+44)/1326=(94+80)/1326=174/1326=13.1% 
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