Converting outs to winning percentages?

[Fade]

Does anyone have a specific way to convert outs into winning percentages on the table quickly?

Thanks in advance.

[arkana]

Very rough approximation is to multiply your outs with 2 if there is one card to come and to multiply your outs with 4 if there are two to come.

If you have 9 outs (for example a flush draw) then you have about an 18% to hit with one card to come and about a 36% chance to hit with two cards to come.

[sinky]

The maths is pretty simple, but after a while you will know the numbers pretty much of by heart. I don't work out percentages, instead I work out odds. It is then much easier to compare with the pot odds.

For example, you have a nut flush draw on the flop. There are 47 unknown cards. 38 of them do not help you, but 9 of them will give you a winning hand. So your odds are 38 : 9 which simplifies to 4.22 : 1. On the turn the calculation is the same except that there are only 46 unknown cards. For this example your odds are 4.11 : 1. Depending on the pot size these odds tell you whether to call or fold.

Percentages are more useful when you are trying to estimate your winning chances for the whole hand. So continuing the example above you have 9 outs and want to know what percentage of times you will hit on either the turn or river. This is calculated as ....
1 - (odds of missing on flop * odds of missing on river)
1 - (38/47 * 37/46) = 0.349 or ~ 35%

This percentage tells you that on average you will win 35% of all future bets in this hand. So if you have 4 opponents who are all likely to call, then you should raise as you are contributing only 20% to get a 35% return.

[Hornsta9]

Hi,

This is something I use to calculate whether the bet is worth taking or not. I am not sure if this is absolutely correct but I am sure one of the more mathmatical of us will say so if I am wrong!

As above, if you have a flush draw and have 9 outs on the flop you multiply 9 by 2 (18%) to get the chance of hitting on the turn, and multiply by 4 (36%) to get the chance of winning by the river.

To apply this to the pot odds I divide that number into 100 (i.e 100/18% = 5.5 or 100/36% = 2.7). This gives you a multiplier to use on your bet to work out whether to call the bet. You multiply the bet by the multiplier and if that number is smaller than the pot you call, if it is larger than the pot you fold. Here's an example

The blinds are 1/2.
You have As7s.
There are 5 people who see the flop with you which makes 6 players in total.
The pot is $12.
The flop is 5s Kc 10s. You have the fllush draw.
1st person to act bets $5 and 3 people call. The pot is now $32.
You have to call $5 and make the pot $37.

To work out whether to do this you should have already calculated your outs (9) and multiplied them by 4 (turn & river to come). This gives you a 36% chance to hit your flush by the river. Now divide 36 into 100, which gives you 2.8 (if you want to be conservative round it up to 3). Now multiply the call you have to make ($5) by 2.8 or 3 (I will use 3 for ease of sums).

This gives sum gives you the number 15. You can only call this bet if the pot is larger than $15, which it is, so call!

Say you call and the turn is Kd. and the pot is $37.

1st person bets $40 and everyone folds to you. Now the pot is $77 and you have to call a bet of $40 making a pot of $117. Using the same formula above you have an 18% chance of hitting your flush on the river and a multiplier of 5.5 (100/18). Therefore 5.5 * 40 = $220.

So you can only call this bet if the pot is larger than $220. It isn't in this example so you should fold.

Obviously this example is just that, an example, and so the betting is not perfect, it is assumed you have no reads and doesn't take into account that even if you hit the flush you might not win!

If your online then have a calculator.

I hope this makes sense but if not then please ask me questions. Also if anyone sees any flaws in these calculations please point them out. I won't be offended!!!

Hornsta!

[chardrian]

It is so interesting to me to see how different people's brains work, and yet still come to the same results.

I happen to think much better in percentages which I then convert to fractions. So yes, multiply your outs by 2 for each street.

I also just think of it as street by street. So in the above example with the nut flush draw I give myself (at least) 9 outs and say I have approximately 18% or about 1 in 5 to hit my spade on the turn. In order to call $5 that means I need the pot to be at least $25 ($5 times 5). It is over $25 so I insta-call.

Some quick calculations that are now just memorized:

flush draw: 9 outs = 18% = 1 in 5
str8 draw: 8 outs= 16% = 1 in 6 (our bet needs to be smaller than 1/6 of the pot in order to call)
two over cards (careful here tho cuz u need to make sure your outs aren't counterfeited): 6 outs = 12% = 1 in 8
middle or low pair (careful again - just looking to hit two pair or trips): 5 outs = 10% = 1 in 10

[Fade]

thanks, that was really helpful.

[Xanadu]

Don't forget to apply your implied odds. A turn call with a 5:1 draw can profitably made with only 3.5-4:1 pot odds.

Top pair outs are usually only worth about half an out each. 2 overs is worth between 3 and 4 outs, not nearly 6. You have 6 outs to top pair, but that will not hold up more than 2/3 or so of the time (very dependant on the board).

Two pair and trip outs are much closer to full value. If you have a pair on the flop, you should count your hand for 4+ outs (if you knew improving would win it would be 5).

Basically, the stronger the hand you are drawing to, the closer to full value your outs have. Obviously draws to the nuts with no outs giving a possibility of a second best hand have full value outs. If your draw is not to the nuts, your outs do not have full value. This is crucially important. Much more so for limit than no-limit, but still very important for no-limit. An example ... you flop an OESD but there are 2 to a flush on board. You have 8 outs to the straight, but 2 of these put 3 flush cards on board. Depending on the # of people in the pot, these 2 cards must be discounted by 1/4-3/4 of an out each. Your 8 out draw may really only be worth about 6.5 outs. A big enough difference to frequently weigh decisions from calls to folds or raises to calls.