Poker is a game of probabilities. Every time when you put money into the pot, you have to ask yourself: what are my odds to scoop the pot? How much to call this bet? How much to bet so that my opponent can not profitably call with his draw?

A lot of questions that are posted on poker forums are of the type: what is the chance THIS or THAT happens? Here are a couple of examples:

1) I have KK and my opponent calls my raise with an Ace. What is the chance that he pairs his ace on the flop?
2) I have a couple of small suited cards. What is the chance that exactly three cards of that suit appear on the board (and not four, because that would mean trouble).
3) I have two unpaired cards. What is the chance that I flop two pair or trips?
4) My opponent raises and could have any two cards doing that. I have a small pair, what is the chance that I flop a set?
5) My opponent raises and I know he only does that with AA/KK/QQ or AK. I have a small pair, what is the chance I flop a set?
6) I have QJ on a T62 flop. What is the chance I make a straight by the river?

For those among you with little affinity for mathematics, these questions could be above your head. So I´m going to provide you with a simple tool that can make these calculations for you.

Create an Excel spreadsheet like this:
In cell H2: the number of unknown cards remaining in the deck,
In cell H3: the number of outs remaining in the deck,
In cell H4: the number of cards to draw,
In cell H5: the number of outs you want to draw in those cards,
In cell H6: the probability that this happens. Paste into this cell the following formula:

=FACT(H2-H4)*FACT(H3)*FACT(H2-H3)*FACT(H4)/FACT(H2)/FACT(H3-H5)/FACT(H2-H3-H4+H5)/FACT(H5)/FACT(H4-H5)

Of course you can use other cells in the spreadsheet to store the data, but make sure you adjust the formula accordingly. Now lets tackle the problems.

1) I have KK and my opponent has Ax, so there are 48 cards remaining in the deck (H2=48). Three of these are aces (H3=3), we will draw three cards (the flop, H4=3) and we want to know the chance that one ace appears (H5=1). In H6 the probability appears: 0.1717 or 17.17%.

2) 50 cards remain in the deck (H2=50), 11 are of that suit (H3=11), draw 5 cards (H4=5) and draw exactly three of that suit (H5=3). The chance is 5.77%

3) We´re getting the hang of it. H2=50, H3=6, H4=3 and H5=2. The chance is 3.37%. This is a pretty important number for those among you that call raises with stuff like suited connectors. At least 1 in 30 times the flop will make you happy (add to this the flops that give you straights/flushes or a good draw).

4) I have a small pair and my opponent raises ATC. He could have the same hand as me and the chance to flop a set would be zero! If he has one of that card, the chance to flop a set will go down significantly. How do we handle this problem? The correct way is to assume that his hole cards are still in the deck. 48 cards remain in the deck, but there are 50 unknown cards and we have to fill in H2=50. The rest is easy: H3=2, H4=3, H5=1. The chance is 11.51%.

5) This is slightly different. We know the opponent has a big hand and all our outs remain in the deck. Whether he has AA/KK/QQ or AK doesn´t matter for the chance to flop our set. H2=48, H3=2, H4=3 and H5=1. The chance is 11.97%. The chance goes up a little, due to your knowledge of your opponents play.

6) This one is pretty hard, but doable with a little logic. The turn has to give us a straight draw, so it has to be a 8, 9, K or A. That is 16 outs. Calculate the chance with H2=47, H3=16, H4=1, H5=1. The chance is 34.04%. You could have calculated this yourself without the spreadsheet (=16/47).

OK, so now we have a straight draw, what do we do with the river? Well, we have an open ender (8 outs) if the turn is a 9 or K or a gutshot (4 outs) if the turn is an 8 or A. On average we have 6 outs. H2=46, H3=6, H4=1, H5=1. The probability is 13.04% (or 6/46).
Combine the turn and river probabilities: multiply 16/47 with 6/46 and you have the answer for your backdoor straight draw: 4.44%. Better than you think, hey?

These were a couple of examples that show the potency of the spreadsheet, combined with your ability of using it correctly. I hope the tool will prove useful for your post-bead-beat analysis!

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