When I tell my non-poker playing friends that I play poker they think I'm gambling - until I give them the following explaination.
Poker, played correctly, is not gambling in my opinion. And I think this is a good way to explain EV to non-poker players or new players. The idea in poker is to do two things - make correct decisions based on available ...
This will be pretty messy if I don't define some variables, so here goes:
P$ = Current size of the pot
S$ = Minimum of your stack vs your opponent's stack
F% = Chance of your opponent folding to your shove (this should be between 0 and 1; divide percentages by 100 to get corresponding value)
W% = Chance of you winning when called (this should be between 0 ...
Probability: the chance of a particular outcome.
More precisely, the probability of any given outcome is the ratio of all the favorable outcomes and every outcome that is possible. (so favorable / everything)
The probability of throwing 6 with a dice is exactly 1/6 because all the sides are perfectly equal, there are 6 of them but only 1 is favorable in ...
The decision is based on the extra equity you gain in the tournament if you win. In the first instance, you have an 80% chance at a 600bb stack, and a 20% chance at not cashing. Your ROI with a 600bb stack would need to go up based on that stack to make the call worthwhile. The breakeven point is
.8 * 300% * advantage + .2 * 300% * 0 = 300%
The left side ...
Say we have a $1 million raffle that has only two tickets: a winner and a loser.
I give you a random ticket and tell you that you MUST sell it. How much money should you sell it for? (I.e. how much is it worth?)
A. $1 million?
No, because it could just as easily be worth $0.
No, because it could just as easily be worth $1 million.
C. $0.5 million?
Running it multiple times does not move EV an inch. It only reduces the variance.
I think the example from kiota is spot on (+1). On the river the number of down cards is 44. Even after you see 2 cards the bet was placed before.
If you hit on the first then you are less likely to hit on the second. If you miss the first you are more likely to hit on ...
If you know your post-flop equity, your cards are irrelevant to the calculation here.
That said, we have one crucial bit of information that is lacking: what range of hands is your opponent reraising with preflop? If he reraises with 100% of his cards and then folds everything but AA/KK, then it's pretty easy to make this profitable. If he only ever ...
There are thumb rules for the preflop equity (against a single random opponent) of pocket pairs and suited-connected combos.
For the equity of a pocket pair, you calculate how many cards away from 2 your cards are (for example, Queens are 10 cards away from 2), multiply by 3 and add 50%.
So QQ's preflop equity is approximately:
(10 * 3) + 50 = 80%
Say that we decide to bet on coin flips.
In the first case, I will give you $1 every time that it is heads, and you will give me $1 every time that it is tails. Simple logic will tell you that since 1/2 of the time I owe you $1 (heads) and the other 1/2 of the time you owe me $1 (tails) that if we flip the coin enough times, it will even out. In this ...
EV does not depend on how many times you run it, only variance does. I will try to illustrate it with a simple example:
Assume heads-up play. You play all-in on the turn and you have x outs to win the hand.
Scenario 1 - Run it once
Cards_left = 52 - 4 (deck) - 4 (in your hands) = 44
P[win] = outs / cards_left = x/44 (you have x/44 equity to win the whole ...
Direct EV calculations are the first step in figuring out how to calculate "maximized EV" based on situational considerations. To become a better player, you will very much care about the size of your positive EV.
Sure, the basic EV calculations say to either bet, call or fold based on card odds vs pot odds. Usually, you're only really looking for a ...
You aren't comparing AKs to any random hand, you're comparing it to a random pocket pair. As per http://www.tightpoker.com/poker_hands.html, the EV of AA-JJ is significantly higher than AKs and as such skews the group "random pocket" enough to be better than AKs.
AKs is still the 5th best starting hand in poker statistically.
First of all it's important to explain that EV is a concept rooted in the law of large numbers, and which poker players use to calculate risk and reward. I'll get back to this concept.
When calculating EV a poker player takes a few things into consideration:
1) The size of the pot
2) The probability of winning that pot
2) The size of the bet they're faced ...
If you have a simple 6 side dice you can arrange a simple demonstration.
Tell your friends you'll give them 1$ in every throw if the result is 3-6, and they have to pay 1$ if it is 1-2.
Tell them you're going to play 5 rounds and what they expect in terms of money won / lost. Then play the game and compare the results to their estimation.
Intuitively they ...
I don't think anything is proven, not even that ev_sb >= 0, so the only bounds we have are trivial: -0.5 <= ev_sb <= 1.
An easier question is "What ev_sb do people find solving abstracted versions of HUNLHE". It would be be interesting to know the sorts of values people are getting, i.e.
1) The value of the (abstract) game from the SB's point-of-...
When holding a pocket pair, you will hit a set one time in 8. That's 12%. Rough math at the table means that you can set-mine if you expect to make 10x your preflop call amount when the set comes (which is going to be a factor of bet-size, stack-size, and opponent tendencies).
KQ offsuit apparently has about 48 - 50 % equity against that range (I calculated this using an equity calculator). So, given that the all-in was preflop, you essentially have a coin-flip. So it's very hard to determine if a call here would be +EV or -EV, especially because figuring out that range is always very hard. So the calculation of equity can (and ...
The book is quite correct -- if your range contains more value than bluffs, then the correct bet sizing is to move all-in.
To see why, consider the classic polar versus bluffcatcher scenario. You have either nuts or air; your opponent's bluffcatchers only beat your air.
The equilibrium is reached in this game under the following conditions. If the pot is ...
Not sure if this is really a paradox, but...
In a heads-up game your opponent truthfully confides in you that he is playing a 100% range.
So you think to yourself, "Great, from now on I will play a 70% range and I will be profitable because I’m ahead of his range."
You are dealt a new hand and see that it is at the bottom of your range, but you no-longer ...
Your question is confusing, and it appears that you may have misunderstood the terminology.
"So I can calculate what the maximum bet size is with a positive EV. However, that would be too high, since we surely don't want a 0 EV."
Do you mean if a bet size is too high, it would not be called, therefore the final value would be zero? This is not the standard ...
The way I understand your question, it seems like b and a are the same thing.
in your example of (a) you mention that the total combinations come out to 42. this number is not arbitrary, it has to come from somewhere. If you were up against a random hand, then there would be a lot more than 42 total combinations. I am assuming that this 42 total ...
Well it seems like you are talking about value betting. The EV is basically if it is worth calling or betting that much. But when you are value betting you should be sure you have the best hand in play. Then the size of the bet is the maximum amount you think your opponent will call.
Say you have the nuts if you are putting your opponent on a strong hand ...
That is a relatively small sample size. I wouldn't worry about it too much if you're thinking that you may have a leak of some sort. I'd say you need tens of thousands of hands before that all-in number starts representing the real EV value. Hands rarely get all in, that's why the sample size needs to be so large.
EDIT: There is a correlation. Leak is ...
It may look easier to you but it's just a mental (mathematical) trick, in fact you're basically stating the same thing:
Consider it like this.
EV > 0
A = (percentage to hit * Pot size)
B = (percentage to not hit * Call size)
EV = (Percentage of hit * Pot size) + -(Percentage of not hit * Call size)
EV = A - B
And with EV > 0
A - B &...
EV = (F% * P$) + (1 - F%) * ((W% * (P$ + S$)) - ((1 - W%) * S$))
this formulae is correct only when P$+S$ = W$,
where W$ is the amount earned at showdown. So this formulae as it is only applies at situations where villain open raises and we shove. As this is not always the case(not always W$ = P$+S$), a more general form of this formulae would be by ...
The EV is (% he folds to All in * Current pot size) + (% of times opponent calls * % you will win * Total size of pot) - (% of times opponent calls * % you will lose * Amount that you bet/shove).
On the left of the "+" sign are the times without a showdown. On the right are the times with a showdown. The times you win or lose can be calculated either ...
You can get some tighter bounds by calculating the expected value of some specific strategy (call it S1), knowing that the GTO strategy will be >= S1. For instance let S1 be the strategy where the small blind goes all-in with AA, and folds all other hands. It is a pretty simple probability problem to calculate the expected values in that situation. There is ...