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To get the probability of the next card being your card that you need, you simply get all the cards that match the definition / total cards not pulled.

However, at river how do you determine your odds of success against an opponent? How does poker TV shows do it?

Once all the hands are shown, it's obvious whose won but before that, they give you a chance of succeeding even at river. How do you calculate your hands success rate at river AND the success rate of your opponents.

All I am able to figure out is that your success rate decreases as more opponents appear and that from my understanding, this seems to be a case of "flipping a coin twice doesn't give you 100% a head".

Is there even a way to predict approximately how much better your remaining opponents have against you? (4 opponents, you got a low card but it looks like there could be a two pair better than you, a flush and maybe another guy has pocket aces)

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On live shows they have the exact hand each player has, so it's much easier to calculate each hand's probability to win. In real life you don't know your opponents exact hand (although sometimes you can guess it), in these scenarios you'll need to play against your opponent's range of hands.

Let's say you have KQo, you need to know how often does your oppenent holds a better king from X position? How often does he have an ace against where your current position is? These questions goes on and on, there are so many variables to take in count but with experience you'll learn to manage them. Let's imagine a theoretical hand example, shall we?

Preflop


Let's say the blinds are 50/100 and you're on UTG+1 with AJo against the BT who seems to be a rag player and the BB who is kind of a loose one. You raise to 385 chips, BT calls and SB calls. Of all the four aces on the deck, you already have one, so you already are 1/4 or 25% favorite, against most of your opponent's range. You can use the list below as a guide to estipulate you equity preflop:

  • Two Overcards against two lower cards (AK vs QJ): 65%
  • Dominating Overcard hand against a hand with a lower kicker (AK vs AJ): 75%
  • One Overcard vs two middle cards (AT vs QJ): 60%
  • Two Overcards against a lower pair (AK vs 55): 45%
  • One Overcard against a lower pair (AT vs JJ): 30%

You can also see other preflop odds examples by going to http://www.parttimepoker.com/quick-tip-preflop-equity-of-common-matchups

At this right moment you have 45.15% equity against the two player's range. The BT's calling range would be something like A7s-A2s, K9s-K6s, Q7s+, J8s+, T9s, A8o-A2o, K6o+, Q9o+, J9o+, T9o and the BB's calling range would also be something like 22+, A2s+, K2s+, Q2s+, J2s+, T8s+, 95s+, 85s+, 75s+, 65s, A2o+, K2o+, Q2o+, J2o+, T8o+, 97o+, 86o+, 76o. You can see that the BB's calling range is much wider than the BT's range, this is because the BB needs to invest only 2.85 blinds related to the pot, which in the above scenarios makes the call profitable.

Flop


The flop comes: A♠7⋄8♥

It's a reasonable flop for you, you are winning most of the time, the only hands that beats you are AK, AQ and you may be against a straight-draw of 9T, 65, 45, 96, 95, etc... You also don't need to worry about the flush-draw right now.

Think about your opponent's range which we stablished before. They may have a better ace, but they also have a much bigger chance to hold something that you beat, such as A9, AT, A6, KQ, KT, QJ, even weaker pairs like 7's or 8's.

At this right moment your equity increased to 71.42% against your opponents. The BB checks, now, you want to bet small because you want to extract value from your hand and get worst hands to call you so you bet 310 chips giving to the BT 20.5% pot odds against his 14.41% equity, he sees that it's not a profitable call and decides to fold. With the BT's fold, BB's equity increases a little bit from 14.15% to 15.94%, still not a profitable call and he folds as well.

Your chances increase because on each street it gets harder for your opponents to have something that beats you.

Let's imagine for a second that either the BT or BB called your bet.

Turn


The turn is a K♠

Your equity went down from 71.42% to 65.47%, this happened because your opponent's range contains some kings and they might get a stronger hand on the river, although, it's most likely they won't.

River


The river is a 4⋄

Now your equity went up a bit to 71.01% compared to your opponent's current range.

It's important to know that each action each player does, helps you to nail down his range, so by the river usually you'll have a closer guess of his hand and also it will be much smaller sized compared to the one we stablished before.

Conclusion


This is how they show on TV, there are computers calculating all the outs on every street for each hand played. I wanted to show you how it works while you are actually playing on your own.

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Without knowledge of other hands you only know what cards improve your hand.

TV knows the other hole cards and cards that have been discarded.

You may be ahead and you just need your opponent not to hit.

You may be dead. Even if you improve you will not be ahead of your opponents current hand.

Some of your outs will be dead meaning it also improves your opponent hand. Say you are on a straight draw and need a T. If your opponent is on a flush draw then T of spades is dead so only 3 outs. Your opponent has an ace and you do not. You do not have a spade. Pair your hole cards is 4. So a total of 7 (good) outs.

In the case of 4 handed and no Ts are out then 6 / 40 = 17.5%.

Your opponent is just 100 - 17.5.

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