Optimal bet system when past results DO influence future results

Last night instead of dealing BJ or Craps, I worked a "window" (just a table) at an event called, "Night at the Races." Kind of simple concept, taped horse races and you are guessing what horse when you make your wager. IOW, there is zero handicapping or anything to go on besides picking a number.

EXCEPT that I noticed the winning number changed every time. At the end of the night I saw that of the 10 horsed running, there were 9 different winners. Some players seemed to "know something" beforehand or who just saw the same pattern I saw. I mean, you didn't need to be a sharp to see this by the 4th or 5th race.

If I am ever a player at one of these my plan is almost set. Except I wonder what the best way to do this is? Martingale is no good as it could take all night to make a win. Go too low and someone else can easily knock you off. So, what would be the optimal betting strategy be for this set of parameters:


1. 10 races, pick by number.
2. Your horse being bet "across the board" paying 3:1 for 1st, 2:1 for 2nd and 1:1 for third.
3. Assume each number "wins" once and place/show will be fairly random.

My guess is somehow choose 3 numbers in race 1, then eliminate that number and pick 3 in race 2, upping your bet each round. But if you had say 50 units to start, how would you bet to get the best result?

Just to check... you can bet any amount, and the idea is to have the best chance for the largest total NOT the best Expected Value for your series of bets (subtly different, cos you might take a more high risk approach)?

The game straight up has a -10% EV (90% return).

If you eliminate one horse from being a winner.... 1/9 * 4 + 1/10 * 3 + 1/10 * 2 = 94% return.

Two horses : 1/8 * 4 + 0.3 + 0.2 = 100% return.

I wouldn't bet at all until the 3rd race. After that, I'd suggest a Kelly, but as you are time limited, I think you'd need to be much more aggressive. A Martingale is never a good system even if you have an advantage.

Plus it's slightly more complicated, as not every horse wins in the ten race set, so it'd be useful to know if there was a minimum time between repeaters (e.g. a horse can't win if it won 1 or 2 races ago... or larger)

If you can bet more than one horse per race, you could consider doing that as well. If horse 8,9 and 10 has not yet won and it's race 6, each is well in your favour as a bet (130% return on each), and you are spreading the risk of losing. Obviously Race 10 as you say can't be a shoe-in for the winner, but I thinking unless you have a big roll at this point, betting large on the final race makes the most sense if your aim is to have the biggest amount of chips.

Just some thoughts.

Do you have to bet on every race? Can you wait until race #8 to bet when you know the last three numbers that have yet to come in? That sounds like the plan. Wait until seven horses won and then bet the mortgage on the other three for the next race. Then the last two for the last race.

It's not clear to me there is an edge. How many races were run? Was it only 9, and each race had a different winner? Or were there many races, and the only thing you know for sure is that the same winner never repeated?

If there were many races, what was the minimum number of races before a horse won a 2nd time? If this is at least 3, then according to math above, there is a small edge.

Some good answers but people had even more questions. So Let me take what was asked by all and try to clairify it:


1. You can bet on as many races as your bankroll will allow. If you want to bet on all 10 you can bet on all 10, though that would guarantee a loss.

2. You can wait as long as you want to bet, there is no miniimum per race.

3. There were 10 races. At the end of the night I counted 9 different winners, no "set" amount of time before a winner could or had to repeat. What seems more clear is that the proprietor of the races probably wanted people who bet one number to hit at least once. Remember, this is all taped races and the "names" of the horses were given locally. For all I know one race could have been taped at Churchill Downs and the next at Saratoga. Betting the number was all that mattered, in fact the names of each number stayed the same all night. So yes, the biggest "inside" thing I knew was numbers did not repeat.

4. Total win is what counts, not EV. Sort of as in a poker tournament you are not getting cash back from your buyin roll, just a prize for winning In this case there was only one winner, but other places may have more so that has to be taken into account. As you probably do not know what everyone else's roll is you cannot do as in "Jeopardy!" and make a perfectly optimal-sized bet to take or protect first place.

5. There seems to be an advantage to betting more horses if you can eliminate the previous winners. Since you are making an "across the board" bet you have a 1 in 5 chance of winning 2:1 and a 1 in 5 of winning 1:1. Maybe someone faster than me can do the math on that part?

The only fact that matters is that you count 9 different winners over 10 races which is a measure of the variance of the result being skewed beyond normal distribution.

The way to bet this is to bet more on numbers that haven't been picked as the races wear on. So, I would bet zero on the first race, and then start betting on "all the other horses" as each race wears on. Assume that there is 10 different horses in each race. Assume that you win 9 units from the winning race and lose on all other horses. I would bet more each race as the chance of other horses being picked decreases.

As I understand it, the 2nd and 3rd place results had no pattern. So we can only change the probabilities for the winner.

Must be a way of changing the actual odds for each race based on previous results, if we assume there's always 9 winners in any set of ten races. Once you have one horse hitting twice in the set, you should know that all the other horses that have won can't win again, so you could then easily make the bets on the remaining "yet to win horses".

If a horse wins race 1, it's not 1 in 10 to win again. There's only a 1 in 9 chance it will win -any- other race at that point. Which would be 1/81 for each subsequent race. The other 9 horses make up the other 80/81. 80/81th divided by 9 = 1 in 9.11 (roughly) So we are at 94% return now on any other horse. So we should skip.

The next race, if there's no repeater, we have two horses that have only a 1 in 8 chance of winning another race.

So 2/64 it's a repeater, 62/64 it's any other horse. 1 in 8.25 it's another horse... 98.4% return on those nags.

Next race... if there's still no repeater, it's 1 in 7 on the first three horses each winning, 3/49, so 46/49 on the rest -> 1 in 6.25 -> 110% return on these horses. Time to start betting. Probably only about 10% of the stake.

Rinse and repeat. As soon as you get a repeater, you should split the race of your bank roll on each of the remaining non-winners. OR take a big guess at one of them for the full stake to try and be the guy with the most marbles... this is the bit that makes it harder to work out a strategy, as even if you know it's one of four horses to win, the only value is having the biggest bank roll, so you might be best to gamble it all on one of those four.