Seven Card Stud Odds and EV

Calculating your odds of completing a winning hand in Seven Card Stud is a more reliable than in Hold´em or Omaha because you get to see more open cards as the hand proceeds. You also get to see the likely odds of another player holding the cards that are required to beat your hand, so learning how to calculate odds is an important factor.

There are many different combinations of how to apply this information, so we will start off with a simple calculation for when you are dealt three of the same rank in your hand, and explain how the odds of getting the card that will give you quads are derived.

Assuming that you are playing a full, eight player, ring or tournament game, when the deal is first made, there are eight cards showing, plus you can also see your two hole cards. So, out of 52 cards in a deck, there are 42 “unseen” cards remaining and you are looking for one card from 42, or 2.38%. After the first round of betting, there are four players left who each receive a card.

Your card does not appear, and now the odds of seeing your card are 1/38 or 2.63%. If the scenario continues through fifth and sixth street, the odds of seeing your missing card turn up on the river are now 1/32 or 3.12%. In reality, the probability of seeing that fourth card is quite small, but you have to reflect on what else is developing in other hands, and you may also have caught a pair to make a full house.

Applying this type of calculation when holding four suited cards, and looking to complete your flush, is more revealing. Let us say that you have your four hearts by the fifth street.

At this stage, there may be two other hearts showing amongst the hands of the three other players still involved at the table, so you can calculate that you have a 7 (hearts remaining unseen) in 34 (unseen cards) or 20.58% chance of catching the missing heart on sixth street PLUS 7/30 or 23.33% chance of catching it on the river if no hearts appear in the penultimate deal – a total of 43.91% or about 5/4 in bookmakers terms. As you have three other players betting into the pot, you are effectively getting 3/1 on a 5/4 chance, and should continue to chase the flush.

The same calculation applies when looking to complete a straight. If you are holding 89TJ by fifth street, and there are two 7s and a Q already showing, there will be 5 cards remaining unseen in a total of 34 unseen cards, which would equate to a (14.71% + 16.67%) 31.38% chance, or just over 2/1.

If you still have three other players in the pot, then it represents value to carry on. However, if one players bets and the next two drop out, you are now in an even money situation holding a 2/1 hand and in negative expected value.

Odds and expected value cannot decide for you whether you should continue to be involved in the hand – only act as a guide. However, it is a fact that players who understand the calculations behind probability and expected value, tend to win money more often than not.

Most Online 7 Card Stud Games are on www.pokerstars.co.uk

Relevant news