How to create a relative ranking of available bets with different return distributions

I am looking for a method/thoughts/ideas on how to create a relative ranking of the attractiveness of available bets, when the odds and probability of winning are "known" or estimated. For example, lets say I have two available bets. Bet 1 pays 2.5:1 with an estimated probability of 50%. Bet 2 pays 15:1 with an estimated probability of 10%. The expected gain is clearly higher on Bet 2 (50%) vs 25% on Bet 1. However, in my opinion such as simple comparison potentially fails to consider things such as length of losing streaks, limited availability to repeat bets, volatility of the equity curve etc. It becomes even more obvious when comparing Bet 1 to a hypothetical 10,000,000:1 with a probability of 1 in 5,000,000. The latter has a higher expected gain but since I would like to be able to enjoy potential winnings in this lifetime, I would like the ranking to show Bet 1 as more attractive or at least require substantially better odds for the long shot bet.

Something like the Kelly criterion could be used to calculate a hypothetical % of bankroll to risk on a given bet when the odds and probability is known and would show that Bet 1 would justify risking a higher % of your bankroll vs Bet 2. However, I am looking to risk the same % on each bet so I guess I am looking for something like the Kelly formula but that can be used to rank the relative attractiveness of the available bets. I have been playing around with weighting the expected gains with the associated probabilities for the bets (essentially counting the probability twice) but I feel like that is overly penalizing to bets with low probabilities of winning.

I welcome any thoughts.

Regards,
Thomas

You make it sound like something to the effect of getting to know the result from figuring probability times potential winnings.. but this is a faulty road to travel because by that logic a player bet in baccarat would look better then basic strat BJ or even the banker bet in bacarat.

Malaru: The types of bets I am referring to would mainly apply to skill based bets such as Sports Betting or betting on horses, where it is theoretically possible to get an edge (positive expected value) by using your own analysis e.g. a horse might have an odds of 15:1 based on the bets placed by the crowd, but if my analysis of that horse and the rest of the field indicates that the probability of that horse winning is 10%, that bet has a positive expected value (or edge) of 50% ((Odds - 1) x probability of win - (1 - probability of win) or ((15 - 1)x 0.1 - (1 - 0.1)= 0.5)), assuming that my analysis of estimating the probability of a given horse winning is valid. I am essentially looking for a way to compare bets, beyond just going by which bet would offer the greatest edge, by also factoring in (among other things) the likelihood of winning since that impacts the volatility of your returns.

The games you mention all have a mathematical probability that is known beforehand and beyond counting cards, you can't impact the expected value (edge) so you would (almost without exception) have a negative edge while playing. Since my initial calculation of expected value is the same as calculating the house edge, using my "logic", assuming 5% commission for 8 deck baccarat (I got the numbers from the Wizard Of Odds web site), the banker bet (expected value -1.06%) or player bet (expected value -1.24%) would only be a better bet if you were playing BJ with rules that would give the house a greater edge than 1.06% or 1.24%.

Regards,

Thomas

Perhaps I am missing something here but I think it is always PayoffAmount Times ExpectationofOccuring. The only variable is that Expectation is a mathematical one or an emotional one. The wheel may or may not actually be biased, but if you think it is, then you are imagining that 7Red will have a greater chance to hit. Or it may be that since red is your favorite color and seven is viewed by you as being your lucky number that 7Red will indeed hit because that little white ball remembers what your favorite color is and will try its best to help you.

The problem arises when there are factors that influence our beliefs. Is the track actually muddy. Does one horse really do better in the mud than the other bettors believe? Is the weather report accurate? Will it begin to rain shortly before post time? When odds are determined by other bettors, knowledge of actual conditions can lead to profits.

When math and luck are the only considerations, I don't see anything but DollarAmount times ChanceofHappening.

I was once in this situation... I was at a casino in Trinidad where they had an American roulette wheel paying 40:1 on the 0 and 00. Player Advantage! So I bought in, put a bet on each, and waited. Spin, no win, repeat. I got bored after about 30 spins and went to play blackjack. I gave up a player advantage because the odds of hitting it were low enough that I hadn't hit it for a while, nor could I expect it to hit any time soon. I was also running out of money...

The lesson here is that the # of times you can make the bet (say... resolutions per hour) & your bankroll are both considerations when analyzing the attractiveness of a bet. For some people, the entertainment value might play into it a little as well.

Instead of looking at the simple expectation of a bet, you should consider (a) whether you will be repeating this bet often (how many opportunities you have and/or how long you will play) (b) what your bankroll is & how big your bet will be.

In a gambling situation, you can calculate an hourly expected loss (or gain), a risk of ruin within your time frame, and incorporate the risk of ruin into your total expectation. I suggest that your hourly expectation, incorporating risk of ruin, is a good way to rank the attractiveness of a repeatable bet.

In a sports betting or prop situation, where you might only get one or very few shots at a bet with an advantage, the wiz has often suggested taking the log of your total wealth as a good indication of happiness. So, although a longshot may pay out a big jackpot, the marginal value of the extra money decreases as you collect more & more. That being said, each person has a different risk tolerance. Two people looking at bets 1 and 2 proposed above might value the two bets differently, based on their risk tolerance. That would be tough to quantify, and impossible to come up with a global rule for ranking prop bets.

Quote: thom321

assuming that my analysis of estimating the probability of a given horse winning is valid.

I think that's a BIG assumption.

Handicappers have forever been trying to do the type of analysis you're talking about. You really think you can do better than what the 'smart money' is doing?

Horses carry a minimum 20% cut that goes to the racetrack which is very hard to overcome. Add the fact that horses are notoriously unpredictable and I think handicapping is a losing proposition.

Sports betting can be overcome but only through some very detailed analysis... the reason for this is that the contest only has two states (win or lose) and there are bets that are habitually not corrected and therefore give the player a slight advantage (see the Wizard's page on Baseball betting) but only when the spread between the losing and winning bet is ten cents or less. When the spread gets higher (generating more win for the house), the advantage disappears. One particular weakness that the wizard picks on is betting the home underdog at baseball games (if the home team is an underdog, bet it).

Quote: boymimbo

Horses carry a minimum 20% cut that goes to the racetrack which is very hard to overcome. Add the fact that horses are notoriously unpredictable and I think handicapping is a losing proposition.

Sports betting can be overcome but only through some very detailed analysis... the reason for this is that the contest only has two states (win or lose) and there are bets that are habitually not corrected and therefore give the player a slight advantage (see the Wizard's page on Baseball betting) but only when the spread between the losing and winning bet is ten cents or less. When the spread gets higher (generating more win for the house), the advantage disappears. One particular weakness that the wizard picks on is betting the home underdog at baseball games (if the home team is an underdog, bet it).

As a veteran horse player, I just wanted to clear something up about the track take. There is indeed a high cut, and one of the biggest cuts comes on the Pick 6 bet (pick the winner of 6 straight races)...BUT, there are often times CARRYOVERS in these situations. If no one Picks 6 on the previous day, 75% of the pool carries over to the next day (25% goes to pay off 5 of 6s, or however many of 6 were the most right)...there is, in fact, a player advantage when the Carryover gets high enough. All of the money is sitting there from the previous day or days. Southern California tracks have regular carryovers in the hundreds of thousands, and usually over a million bucks a couple three times a year. If you search for Carryovers, you can make random picks and have a player advantage. Remember, you'll win whatever the pool is divided by the number of winners. When I hit one last year for $15000, there were 5 other winning tickets. BTW it was a $720 ticket (360 combinations) that I won with (all Pick 6 tickets are $2 except for a few rare tracks)....