Nathan Tyree: Spain
Roulette pays 35 to 1 (normally), which sounds like a big pay out. If I bet $1 and win I get $35 in return. The problem is that a roulette wheel has 38 spaces, each equally probable to turn up on any given spin. I should expect to win once out of every 38 attempts, which will cost me $38. The single win I expect will pay $35, leaving me with an expected return of -$3 on each 38 attempts. It is easy to see that any wager with a negative expectation is a bad wager to make, so roulette is a poor risk to take.
I good bet is one in which you have a positive expectation. For instance, playing Texas Hold ‘Em, a starting hand of A-A is very likely to win. It is the nature of that game that (assuming you are playing multi-handed and not heads up) you will win much more when you do win, than you will lose on your failed attempts. I’ve simplified the following numbers, but they are not far off. A-A will win about 35% of the times that you are dealt them. It is the nature of small stakes games ($2/$4, $3/$6, $4/$8, $5/$10 are the most common of these games) that many players will invest in nearly every pot, meaning that on those times when you are dealt pocket aces your investment in the pot is likely to be somewhat less than ¼ of its total. Your return on this bet should be 4 to 1, but you should win slightly more than once every three attempts.* It is easy to see that in this case you have a positive expectation, and therefore a good bet. Every action in poker should be looked at in this way. A good player makes moves that provide a positive expectation (over time) and avoids ones that have a negative expectation.
In other news, Sometimes She Dreams of Spain is up.
*Actually, Aces will win more than 35 percent of the time. I've left out of the calculation those times that an early raise by the player with aces drives out the entire field, allowing that player to take the blinds. Obviously this skews the data a bit as it increases the winning percentage, but also decrease the average pay out for the hand
Tags (beta): poker
Roulette pays 35 to 1 (normally), which sounds like a big pay out. If I bet $1 and win I get $35 in return. The problem is that a roulette wheel has 38 spaces, each equally probable to turn up on any given spin. I should expect to win once out of every 38 attempts, which will cost me $38. The single win I expect will pay $35, leaving me with an expected return of -$3 on each 38 attempts. It is easy to see that any wager with a negative expectation is a bad wager to make, so roulette is a poor risk to take.
I good bet is one in which you have a positive expectation. For instance, playing Texas Hold ‘Em, a starting hand of A-A is very likely to win. It is the nature of that game that (assuming you are playing multi-handed and not heads up) you will win much more when you do win, than you will lose on your failed attempts. I’ve simplified the following numbers, but they are not far off. A-A will win about 35% of the times that you are dealt them. It is the nature of small stakes games ($2/$4, $3/$6, $4/$8, $5/$10 are the most common of these games) that many players will invest in nearly every pot, meaning that on those times when you are dealt pocket aces your investment in the pot is likely to be somewhat less than ¼ of its total. Your return on this bet should be 4 to 1, but you should win slightly more than once every three attempts.* It is easy to see that in this case you have a positive expectation, and therefore a good bet. Every action in poker should be looked at in this way. A good player makes moves that provide a positive expectation (over time) and avoids ones that have a negative expectation.
In other news, Sometimes She Dreams of Spain is up.
*Actually, Aces will win more than 35 percent of the time. I've left out of the calculation those times that an early raise by the player with aces drives out the entire field, allowing that player to take the blinds. Obviously this skews the data a bit as it increases the winning percentage, but also decrease the average pay out for the hand
Tags (beta): poker
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This is where your judgement on these matters fails. You should not expect this.
38:1 odds do not mean that your number should come up once in every 38 spins. They mean that you are 37 times more likely to loose on each spin.
However, you could get lucky and hit the same number 5 times in a row. (That would mean that at least five other numbers wouldn't be showing up in the set of 38 that we're currently in).
I'd like to see your concept of odds applied to horse racing.