Percentage to Odds Help

[player1]

hello,

i could use some help converting percentages (pot equity?) to odds.

for instance:

random hand vs 72o -> 65.4% vs 34.6% (pot equity)

does this also mean:

65.4/34.6 -> 1.89 to 1 (random hand's advantage over 72o)?

SB/BB example:

everyone folds to me (SB) and i only have just enough to call the BB. if i have 72o, am i correct to call allin since i'm getting 4:1 if i go allin (since i'm only a 1.89:1 underdog to a random hand)?

i guess my main question has to do with pot equity %s and how it translates to X to Y odds. if you could confirm/correct my example, i would really appreciate it.

thank you,
jc

[Lost Wages]

You got it. If the probability of an event is P, then the odds against it are (1-P)/P:1.

In the small blind example you are getting 3:1 if the big blind is 2x the small.

Lost Wages

[Mike Haven]

apart from the fact you would be getting 3 to 1 pot odds, not 4 to 1, you are correct, if you were going to be all in by completing the small blind (edit: in the small blind example you are getting 3:1 if the big blind is 2x the small blind, per Lost Wages)

you would win 1.5 small blinds 35% of the time = 0.525sb, and you would lose 0.5sb 65% of the time = 0.325sb, yielding a long term profit of 0.2sb per all in call

i can't imagine that you would find yourself in that position too often in reality!

[player1]

thanks Mike and Lost Wages!

Mike, you said:

"you would win 1.5 small blinds 35% of the time = 0.525sb, and you would lose 0.5sb 65% of the time = 0.325sb, yielding a long term profit of 0.2sb per all in call"

first, did you mean 1.5 big blinds? if so, i'm not sure why it would be 1.5 and not 2.0 (the size of the pot after i call)?

you're right though, i really shouldnt be in this situation. sometimes i forget (gunshy) to raise before the blinds get to me in STTs.

thanks again,
jc

[Mike Haven]

sorry - i used the wrong jargon, using "blind" instead of "bet"

the big blind posted 1 small bet; the small blind posted half a small bet - therefore there are 1.5 small bets in the pot (if the game is 10-20 the 10 is the small bet; the 20 is the big bet; the small blind would post 5, half a small bet)

when you calculate pot odds you look at what is in the pot BEFORE you put your money in

so if you are the small blind, you have to call half a small bet to win one and a half small bets (in our 10-20 game there is 5 + !0 = 15 in the pot - you have to put in 5 to win the 15 in the pot - you are getting 15 (existing pot) to 5 (your bet) pot odds = 3 to 1

yes, you may win a pot of 20, but only 15 is profit at the point where you made the decision to enter the pot (your previous 5 is not yours any more - it belongs to the pot, so it is part of the 15 "winnings" you are trying to make with your new addition of 5)

also, perhaps more important, when i said you won't find yourself in that position very often, i meant that you won't very often have only 5 left (in our 10-20 game) so that your completion of the small bet leaves you with no chips and therefore all in - you are not all in if you have more chips left

if you have more chips left, entering the pot with the cards you mentioned is not a good bet (imo), not because you won't win enough times if you see all the cards, but because you will be forced to fold on the flop or the turn or the river because of bets made by your opponent that you cannot and should not call at those points in the hand, even though your cards would have won (by some fluke or other) had you called (apparently badly) and completed the hand

the answer i gave applies only when you are paying to see all the cards with that particular bet - that is, when you are all in, no chips left