This is a discussion on Bet Evaluation without Odds within the online poker forums, in the Cash Games section; For the mathematically challenged, learning to estimate Poker odds can be a nightmare. The math may be simple enough, but the calculations are often too 


#1




Bet Evaluation without Odds
For the mathematically challenged, learning to estimate Poker odds can be a nightmare. The math may be simple enough, but the calculations are often too difficult to perform under time restraints. Poker expert Phil Gordon has tried to remedy this situation by introducing the rule of 4 and 2 – a valuable tool to determine the chances of making your hand. Regretfully, it can still be a hassle to evaluate your bet, because of the mental leap between percentages and odds. Moreover, division can be a tricky operation to carry out – as opposed to multiplication.
After some research, I have found a way to evaluate bets using simple addition and multiplication. First, you apply Gordon’s rule, i.e. multiply your outs by 4 or 2, for the chance of making your hand after two or one cards, respectively. Then look up the resulting percentage in the following easily memorized table: Code:
% n  50 2 33 3 25 4 Notice how % x n = +/ 100 20 5 17 6 The table simplifies what would have 14 7 been a timeconsuming division. 13 8 11 9 10 10 9 11 For example: You’re in a $2$4 Limit Poker game, at the turn. The current pot contains $14, and you predict the final pot will contain $30. You’re one suited card short of a flush, so you have 9 outs – which means your chance to win is about 18%. You multiply your $4 bet by 6, for a projected breakeven pot of approximately $24. Conclusion: your bet is justified. 
#4




Another example.
Flop You have 5 outs. Gordon's Rule of 4 5 x 4 = 20% The chances of making your hand by the river are 20%. Table Code:
% n  50 2 33 3 25 4 20 5 17 6 14 7 13 8 11 9 10 10 9 11 BreakEven Pot Your bet is $4. $4 x n = $4 x 5 = $20 Final Pot There is currently $8 in the pot from your opponents. With your bet, that amounts to (at least) $12 in the final pot. Conclusion You won't be able to break even. $12 < $20 You should fold. 
#5




re: Poker & Bet Evaluation without Odds
Quote:
If you are going to refer to a table.. then why not just have a table of outs to odds??? Why bother calculating outs to precentages and then using a table to lookup percentages to odds??? It may be aimed at the mathmatically challanged, but could only be sold to the logically impaired!! LOL This might be handy http://www.texasholdempoker.com/odds_chart 
#6




Quote:
For example: The chance of making your hand is 20%. So, to break even in the long run, your share in the pot cannot exceed 20%. What should be the minimum size of the pot in this case? 20% x 5 = 100% Let's say your bet is $4. $4 x 5 = $20 The projected breakeven pot is $20. Bet Evaluation without Odds In summary, there are two calculations to be performed: 1) The chance of making your hand. Most people seem to prefer calculating odds in stead of percentages, but percentages offer the advantage that you can use Gordon's rule of 4 and 2. 2) The size of the breakeven pot. Calculating pot odds is kind of illogical, since odds are about probability, and unless you include implied bets, calculating pot odds has nothing to do with probability. By calculating pot odds you wish to find out what the ratio is between your bet(s) and your possible winnings. Pot odds are called pot odds, and not pot ratio, because they're meant to be compared to the odds of making your hand. Anyhow, it seems more logical to me to translate the chance of making your hand to a projected breakeven pot, than to translate the actual pot to odds. Of course, you can do it either way, and the result will be the same. 
#7




Quote:
Quote:

#8




Quote:
You ask yourself: "how big does the pot need to be for me to call or raise?"  the answer is the projected breakeven pot. Then you can start thinking about implied bets, i.e. speculating as to how big the final pot will be. 
#10




re: Poker & Bet Evaluation without Odds
Quote:
True, but people do take the pot size into account. I'm just suggesting an alternative way to link the chances of making your hand to the pot size. This does not affect other strategic considerations. 
#11




Quote:
Quote:
Im not even sure why it is easier for you to calculate one and not the other. Thats the bit I just dont understand. It requires the same mathmatical operations to do either. If it works for you then thats good, but I cant see the advantage. The disadvantage would be that everytime you read a staratagy based on poker maths, you will have to convert it as the convention is to talk in terms of odds rather than future pot size. 
#12




Let's run through my original example again:
You’re in a $2$4 Limit Poker game, at the turn. The current pot contains $14, and you predict the final pot will contain $30 (including $4 bet). You’re one suited card short of a flush, so you have 9 outs. Approach 1: Odds There are 9 cards out of the remaining 46 cards that will make you win. 46  9 = 37 37 cards will make you lose. Your odds are 37 to 9. 37 / 9 = ? Wait ... 9 x 4 = 36 Your odds are about 4 to 1. Your bet is $4, and the final pot $26 (excluding $4 bet). 26 / 4 = ? Wait ... 6 x 4 = 24 The pot odds are about 6 to 1. 6 to 1 > 4 to 1 Your bet is justified! Approach 2: Percentages According to Gordon's rule of 2 ... 9 x 2 = 18 ... your chance of making your hand is 18%. 100 / 18 = ? Wait ... 17 x 6 = 100 You need to win 6 times your bet to break even. 4 x 6 = 24 The breakeven pot is $24. Your bet is $4, and the final pot $30 (including $4 bet). $30 > $24 Your bet is justified! Differences 1) In my approach, the actual pot isn't used for any calculations  it's just compared to the breakeven pot in the end. Note that because I'm not interested in the pot odds against me, I can include my current bet into the final pot. 2) Odds calculations have a substraction and two disivions, my percentages calculations have one division and two multiplications. Arguably, division is the most difficult operation, so ... 
#13




Quote:
TBH once you get more familiar with outs to odds, you just learn them and dont really calculate the hand odds anymore. There are only about 20 to learn, after about 15 they are just fractionally lower than the previous and all under 2:1. Personaly I'd stick with the traditional method.. in the longrun you will find it easier. For me to do the same thing.. I look at the pot size, and divide it by the bet i have to call.. I get a pot odds figure. Say 6:1 I just know that 9 outs gives me just over 4:1 (you could use a table for this to begin with) Here is such a table http://www.texasholdempoker.com/odds_chart?chance_format=odds_against&decimals=2 so I compare 6:1 to 4:1 and then know I am in an situation with correct odds. Its not as complicated once you start remembering odds. I think its very good that you are taking the time to figure stuff out for yourself, its something that I do all of the time. I think it makes you a much better player because you will have a deeper understanding than someone who blindly excepts what they are told. Often I find that I my initial idea was wrong.. figuring that out also increases my knowlege. However there is no need to reinvent the wheel!! 
#15




re: Poker & Bet Evaluation without Odds
Quote:
One more question, though. If I understand correctly, the following equation needs to be true: Code:
winnings  > odds against winning bet Would the following, mathematically derived equation be good, too? Code:
winnings > bet x odds against winning 
#16




No probs
Yeah that would work. I would still suggest looking at it in the form of odds.. once you get better at that you will be able to see an opponent make a bet and know the odds he was getting, thus determine how much he chases draws or how he sees players in terms of implied odds.. But for the purposes of seeing whether or not you are getting correct pot odds to call.. yes it is correct. The other thing to remember is you dont have to be 100% exact on calculating pot odds, by using the rule of 2 and 4 you introduce some inacuracy into the calculating of the hand odds.. but its not a problem, its a good aproximation of the hand odds. The same is true of pot odds, with the situation above where you got 6:1 pot odds and hand odds of a little more than 4:1, you would have to seriously over aproximate the pot odds to get a figure which would lead you to the wrong decision. Say you are faced with calling a 430 bet for a pot of 1560.. its about 4:1, because the denominator (430) was rounded down id say its a bit under the 4:1 maybe as low as 3.5:1.. its just a guess. The actual answer is 3.62:1.. Im happy with thinking its a figure between 3.5  4 : 1 (just punched it into a calculator) We are being offered 6:1 its no where near.  easy call 3.5:1  Id probably still call .. its mathmatically incorrect, but its not that much of a mistake. And when playing thats probably as accurate as my maths is.  Im saying this just incase you are trying to be too accurate. Once you start calculating things beond half an odd.. i.e 2:1, 2.5:1, 3:1, 3.5:1 then its just overkill. In the aboveexample I knew it was a bit under 4:1 so I opted for 3.5:1 It just seemed correct.. as it turned out it was good enough. 