Hedging a sports bet
Quote: billryanLet's say someone placed $20 on the Golden Knights ,as a lark, at 200-1. There are now eight teams left. If they survive this round they will be one of four . Does it make sense to hedge by betting on the other three. If so, how would you do it?
I believe there are still seven other teams remaining. Personally, I would wait until after this round when there are just three other teams remaining. Propswap.com is also an option to sell the ticket. I do not know what types of fees they charge.
Quote: billryanLet's say someone placed $20 on the Golden Knights ,as a lark, at 200-1. There are now eight teams left. If they survive this round they will be one of four . Does it make sense to hedge by betting on the other three. If so, how would you do it?
A winning ticket would be worth $4,020. Unless that is a life-changing amount of money to you, I'd not hedge and take your chances. However, if you must hedge, I would bet the opposite to team win every series. Assuming each series is roughly 50/50, I'd bet
$550 on series 1
$1100 on series 2, if comes to that.
$2310 on series 3, if it comes to that.
I would not make futures bets on the other teams, because there is much higher house edge on futures. Around 25%, compared to 5% on a money line bet.
Again, I don't recommend hedging.
Quote: billryanLet's say someone placed $20 on the Golden Knights ,as a lark, at 200-1. There are now eight teams left. If they survive this round they will be one of four . Does it make sense to hedge by betting on the other three. If so, how would you do it?
As always when it comes to hedging, you have to decide if the amount of money at stake, in your example $4000, is enough to be 'life changing', or how about just 'a really big deal'. If you are a guy who makes 4 figure bets with regularity then I would say no, don't hedge, as the hedge by definition on its own would be a negative EV bet. However, if you are a guy who makes $600 a week and winning even $1k lets you go on a trip you otherwise couldn't afford, then here is a plan.....
If they are even money against the team they face in the semifinals, bet $1100 to win $1000 against the Knights.
If the Knights lose you at least walk away with $1000.
If they win you now bet $1980 to win $1800 on the team they face in the finals.
If the Knights win you will have lost 1100 +1980, but won 4000, so plus $920.
If the Knights lose you win 1800 but lost 1100 so plus $700.
So 50% chance you win $1000
25% chance you win $920
25% chance you win $700
You can change the amount you want to hedge at your leisure......
Quote: billryanLet's say someone placed $20 on the Golden Knights ,as a lark, at 200-1. There are now eight teams left. If they survive this round they will be one of four . Does it make sense to hedge by betting on the other three. If so, how would you do it?
With all due respect to the Wiz, I disagree on not hedging. You put in your wager / risk, and now you are in a position to make a profit regardless of outcomes. I always take a profit when it is on the table... regardless of dollar amount.
You have the opportunity to bring back 4020 if LV wins it all. You are in a great position to hedge because LV is favorite and the hedge value is smart money for you.
- Current series against San Jose. SJ is Plus 1500. I would put a small amount on SJ (50) for the series. This way, if for some fluke reason SJ wins, you at least put 730 in your pocket for your awesome decision to pick LV early in the season. You at least have something to show for it.
- Next series will be against either Jets or Predators. Odds are unknown but LV will be at least even or favored. You will be in for 70 already this point. Now I would bet the other side on series for a few hundred depending on odds. Again, you will at least make a few hundred bucks regardless of outcome.
- Now you are at Stanley cup and in for lets say 370, but a win of 4020 is still alive. Now I would bet anywhere from 1000 to 2000 on the other side of series if you are favored or even.
Guaranteed profit is always a good hedge when the alternative is a loss... in my opinion.
Quote: WizardA winning ticket would be worth $4,020. Unless that is a life-changing amount of money to you, I'd not hedge and take your chances. However, if you must hedge, I would bet the opposite to team win every series. Assuming each series is roughly 50/50, I'd bet
$550 on series 1
$1100 on series 2, if comes to that.
$2310 on series 3, if it comes to that.
I would not make futures bets on the other teams, because there is much higher house edge on futures. Around 25%, compared to 5% on a money line bet.
Again, I don't recommend hedging.
Alot can change between October and April. What if in a case like this the person believes a different team has a good shot at winning the championship? Or what if they just put the 20 bucks on Vegas as sorta a novelty bet.. (many did this from what the sportsbooks are saying ).. and not necessarily because they thought it was good odds or even a smart bet ?
Quote: WatchMeWin
Guaranteed profit is always a good hedge when the alternative is a loss... in my opinion.
For a casual bettor this can be an ok philosophy. But for someone who does it for a living (an AP) it is 100% wrong. Each bet should be evaluated on its own merit. Whether or not you have a future bet on Vegas has ABSOLUTELY NOTHING to do with whether or not betting against them in this round is a good bet. As always, the purpose of the bet and it's context need to be evaluated. For me, I would probably hedge a little. KNOWING in pure EV terms it is not wise, my personal desire to WIN even a little outweighs the lost EV I will surrender by making a 'bad' bet. To someone like Axel or Wiz the EV outweighs the 'feeling'. To me (and I guess you too, WMW), the feeling outweighs the EV.
It is the same reason I occasionally (rarely, actually) play the lottery. The feeling outweighs the -EV.
Quote: WatchMeWinWith all due respect to the Wiz, I disagree on not hedging. You put in your wager / risk, and now you are in a position to make a profit regardless of outcomes. I always take a profit when it is on the table... regardless of dollar amount.
Indeed, we will just have to disagree here. This is the same argument used to accept "even money" in blackjack. Those with a long-term perspective usually come out ahead in the long run.
Actully, I have commented on this hedging thing many times. I think hedging is ok in certain situations. AS LONG AS YOU HAVE AN OVERALL ADVANTAGE IN THE FIRST PLACE and hedging doesn't cost you more EV than you had in the first place.Quote: SOOPOOFor a casual bettor this can be an ok philosophy. But for someone who does it for a living (an AP) it is 100% wrong. Each bet should be evaluated on its own merit. Whether or not you have a future bet on Vegas has ABSOLUTELY NOTHING to do with whether or not betting against them in this round is a good bet. As always, the purpose of the bet and it's context need to be evaluated. For me, I would probably hedge a little. KNOWING in pure EV terms it is not wise, my personal desire to WIN even a little outweighs the lost EV I will surrender by making a 'bad' bet. To someone like Axel or Wiz the EV outweighs the 'feeling'. To me (and I guess you too, WMW), the feeling outweighs the EV.
It is the same reason I occasionally (rarely, actually) play the lottery. The feeling outweighs the -EV.
Guaranteed money can be invested into other plays at even a better rate. A bankroll bump may not change your life but it could change what you are now willing to play/invest in, thus increasing earn rate going forward.
There are also emotional aspects of having money in your hand. It oftentimes adds motivation to playing more and seeking out opportunities.
I have a question for the Wizard. I don't know what your risk tolerance is or what a significant amount of money is too you. Let's say we are talking about risking 200k(I don't think that would change your life). let's say there's a play where they have a promotion on roulette where you could guarantee yourself a profit of 5% without any risk by hedging black/red cover green. Or you could make 7% with a huge amount of risk. What do you choose?
I will give another example. This really isn't hedging per say, but you can see where in going. Let's say there's a situation on VP where you can earn 8% in EV but you have to get a dealt Red Royal or you can make 5% and all the EV is coming from hitting 4 of kinds. What do you choose?( just assume risk isn't a factor on this)
I chose the smaller percentage and earn in both cases.
From my non-AP perspective, I would only consider hedging if I can lock in a guaranteed win. So for this bet I would wait until the finals or maybe even until they (VGK) face an elimination game in the finals.
Quote: SOOPOOFor a casual bettor this can be an ok philosophy. But for someone who does it for a living (an AP) it is 100% wrong. Each bet should be evaluated on its own merit. Whether or not you have a future bet on Vegas has ABSOLUTELY NOTHING to do with whether or not betting against them in this round is a good bet. As always, the purpose of the bet and it's context need to be evaluated. For me, I would probably hedge a little. KNOWING in pure EV terms it is not wise, my personal desire to WIN even a little outweighs the lost EV I will surrender by making a 'bad' bet. To someone like Axel or Wiz the EV outweighs the 'feeling'. To me (and I guess you too, WMW), the feeling outweighs the EV.
It is the same reason I occasionally (rarely, actually) play the lottery. The feeling outweighs the -EV.
I understand your reasoning. For me, it is principle to lock up a W whereas there is a real chance to losing money instead of making money in the event. Just as in the stock market, the principle is to take profit and offset any risk of losing money if the scenario presents itself. Of course, value and expected return is taken into consideration. Im not saying to hedge a great amount.... just enough to ensure a W regardless of the outcome while still allowing a large payout W if the original wager is won. The 'feeling' aspect is secondary to the 'bottom line' for me. Sure I enjoy the entertainment along the way, but at the end of the day, its all about the benjamins! Ive been rich... and Ive been poor. I can say for certain that life is a whole lot better when you have money.
Quote: WizardIndeed, we will just have to disagree here. This is the same argument used to accept "even money" in blackjack. Those with a long-term perspective usually come out ahead in the long run.
.... but what if in your blackjack comparison you were to lose your initial bet instead of pushing if the dealer pulls over a bj also? This is more of a parallel scenario to the hedge described. Do you risk taking and L?
Quote: WatchMeWinWith all due respect to the Wiz, I disagree on not hedging. You put in your wager / risk, and now you are in a position to make a profit regardless of outcomes. I always take a profit when it is on the table... regardless of dollar amount.
You have the opportunity to bring back 4020 if LV wins it all. You are in a great position to hedge because LV is favorite and the hedge value is smart money for you.
- Current series against San Jose. SJ is Plus 1500. I would put a small amount on SJ (50) for the series. This way, if for some fluke reason SJ wins, you at least put 730 in your pocket for your awesome decision to pick LV early in the season. You at least have something to show for it.
- Next series will be against either Jets or Predators. Odds are unknown but LV will be at least even or favored. You will be in for 70 already this point. Now I would bet the other side on series for a few hundred depending on odds. Again, you will at least make a few hundred bucks regardless of outcome.
- Now you are at Stanley cup and in for lets say 370, but a win of 4020 is still alive. Now I would bet anywhere from 1000 to 2000 on the other side of series if you are favored or even.
Guaranteed profit is always a good hedge when the alternative is a loss... in my opinion.
How are you sure LV will be favored against Winnipeg or Nashville? I say they are underdogs.
I'd wait to hedge until the next round or the Cup finals if I had $4000 waiting for me.
Quote: FinsRuleHow are you sure LV will be favored against Winnipeg or Nashville? I say they are underdogs.
I'd wait to hedge until the next round or the Cup finals if I had $4000 waiting for me.
In between the first and second rounds, most books had the knights listed as favorites to win the Cup. So I’m assuming that implies they’d be favored in any series going forward. Unless there’s an injury. Or perhaps if they squeaked by San Jose in 7 while Winnipeg or Nashville swept the other.
Quote: FinsRuleHow are you sure LV will be favored against Winnipeg or Nashville? I say they are underdogs.
I'd wait to hedge until the next round or the Cup finals if I had $4000 waiting for me.
Im not big on NHL so I just took a look at the current NHL lines for Stanley Cup. LV was the most favored at 4-1 , with Jets being 6-1 and Predators being 9-2.
Quote: WatchMeWinIm not big on NHL so I just took a look at the current NHL lines for Stanley Cup. LV was the most favored at 4-1 , with Jets being 6-1 and Predators being 9-2.
I'm pretty sure the reason for that is that the Jets are playing the Predators. It's a harder series than Vegas against SJ. Predators are definitely favored against Knights. Jets/Knights would be pretty close.
And VGK already won game one last night. Before the second round started it was Nas favored. (But it was close).Quote: FinsRuleI'm pretty sure the reason for that is that the Jets are playing the Predators. It's a harder series than Vegas against SJ. Predators are definitely favored against Knights. Jets/Knights would be pretty close.
Quote: billryanLet's say someone placed $20 on the Golden Knights ,as a lark, at 200-1. There are now eight teams left. If they survive this round they will be one of four . Does it make sense to hedge by betting on the other three. If so, how would you do it?
It depends on your goals. I have broken with the "shall not hedge" commandment before. My reasoning is I come from a finance background and look at bets like stocks and options. If you can make a guaranteed win, I say go for it as it is good risk management.
But in the end, you just gotta decide on the bigger possible win vs the guaranteed win.
Most of the time, your edge on a sports bet will be small and you often give some of it back to the book by hedging. One way around this is to pre hedge by betting a smaller amount. Think ahead and bet only to win an amount you won't want to hedge. That way you hedge for free.
There will be times where good line shopping allows you to give back a very small amount, nothing or even be +ev . Just keep looking till you find something good and if you don't, roll the dice. With a series bet, you will have multiple chances to find something.
I broke all my own laws and bet the cavs when the westgate had them 12-1 after taking a huge bet on the rockets. It was an outlying number, but i bet hoping for the scenario above. Can't remember last time i did that and it ain't looking good.
Quote: WBGambleI think whoever wins the WPG-NSH series will be a favorite over VGK-SJ. The $ on Vegas could be influencing the line a bit, making fading VGK next round a reasonable bet on its own. I would start considering a hedge only at the conclusion of this round. $500ish value is too low to start hedging
The books are in big trouble if Vegas wins because so many people put $10-$100 on them to win the cup. But at this point, some people are going to start hedging. I think this will create value, but I'm not sure which way. Do the books want to entice people to hedge by offering juicier odds on NAS/WPG, or do they think so many people are going to be hedging that Vegas is actually a good play next round?
Quote: AxelWolfI have a question for the Wizard. I don't know what your risk tolerance is or what a significant amount of money is too you. Let's say we are talking about risking 200k(I don't think that would change your life). let's say there's a play where they have a promotion on roulette where you could guarantee yourself a profit of 5% without any risk by hedging black/red cover green. Or you could make 7% with a huge amount of risk. What do you choose?
I will give another example. This really isn't hedging per say, but you can see where in going. Let's say there's a situation on VP where you can earn 8% in EV but you have to get a dealt Red Royal or you can make 5% and all the EV is coming from hitting 4 of kinds. What do you choose?( just assume risk isn't a factor on this)
I would do the one where the ratio of advantage to variance is more.
Quote: KeeneoneRS made a nice post about this from a math/AP perspective In a past thread. Short answer = don’t hedge.
From my non-AP perspective, I would only consider hedging if I can lock in a guaranteed win. So for this bet I would wait until the finals or maybe even until they (VGK) face an elimination game in the finals.
I actually kinda forgot about making that post and was considering (re)-writing it. But yeah, from an AP perspective, you're pretty much never going to want to hedge, at least that shouldn't be your game. Of course sometimes things change...but the requirement to hedge should be more than just "I have X leg(s) to go on this parlay/series" or what-have-you. But to rehash what I wrote before a bit...and without doing lots of math and whatnot....it's rather likely that the SUM of your +EV bet and the -EV from hedging makes it an overall -EV proposition as a whole.
Here's an example, not related to sports betting, but kinda related, so you can see exactly what the math looks like. Let's say you can make a bet that someone will flip a coin (50/50) to land on heads 10 times in a row. The probability of that is 1 in 1024 (2^10 = 1024). If the coin lands on tails within 10 flips, you lose your wager and you may bet again. If there are 10 heads in a row, you are paid and it is settled and you may bet again on another set of 10 flips. You are getting paid 1,050-for-1. So for every 1,024 trials, you'll get 1,050 wagers back, profiting 26 units. That's ~2.53% advantage. The hedging part: you can bet on any single coin-flip, either side, at -110 odds. You decide to lay $550 to win $500 if/when you get to 9-in-a-row.
In a cycle of 1,024, betting $1 per trial, you would make the $550 lays twice -- one wins, the other loses. Well, that means you'll lose $50 per 1024 trials just from hedging. Your EV is $26 per 1024 trials. Add those numbers up, and now you're looking at a -$24 in EV for the 1024 trials (1 cycle). Now instead of having a 2.53% advantage you have a disadvantage.
Of course, that isn't to say you should never hedge, just that it shouldn't be in your game plan, unless you calculate it ahead of time and are aware going into it. Sometimes things change and you may be better off to hedge off your exposure to just guarantee a (smaller) loss.
But if you're at the point where you're thinking, "Wow, I have so much potentially riding on this last game, I should hedge" then you should'a just bet less to begin with.
From just a gambling-for-fun perspective, do whatever the hell you want.
Quote: WizardIndeed, we will just have to disagree here. This is the same argument used to accept "even money" in blackjack. Those with a long-term perspective usually come out ahead in the long run.
.... but what if in your blackjack comparison you were to lose your initial bet instead of pushing if the dealer pulls over a bj also? This is more of a parallel scenario to the hedge described. Do you risk taking and L?
Help me understand why you would risk taking an L, when the alternative results are W's regardless of outcome. I understand the risk value vs payout value but principle of the matter should always hold true.
In his example of having 20 on the LV to win 4000 in stanley cup, wouldn' the following scenarios be better at start of playoffs where so many unknowns in several series of play with high probability of losing initial 20 bet.
- either win 700
- or win 700
- or win 2000
as opposed to not hedging and having a lower probability of success getting to the SC and winning it:
-either lose 20
- or win 4000
What if you had 2000 on the ticket to win 400,000.... does this change your hedging opinion?
Quote: WatchMeWin....
Help me understand why you would risk taking an L, when the alternative results are W's regardless of outcome.
What if you had 2000 on the ticket to win 400,000.... does this change your hedging opinion?
To answer the first question, every time you make an individual bet you are risking taking an L. That's what gambling is. You have made that bet presumably because you think the chance of a W exceeds that of an L, or that you were getting enough odds to make it a positive EV bet.
The fact that you have a previous bet which now has a substantial positive EV does not affect the EVof any subsequent bet.
As far as your second question, if the few hundred thousand you could lock in by giving up the chance to win the 400,000 is a significant amount of money to you and you would do something with thatfew hundred thousand then it might make sense for you to give up the EV. My guess is if you were a betting $2000 on a future bet at 20 to 1 odds the few hundred thousand dollars although a very nice pay day is probably not a life-changing pay day.
Quote: SOOPOOTo answer the first question, every time you make an individual bet you are risking taking an L. That's what gambling is. You have made that bet presumably because you think the chance of a W exceeds that of an L, or that you were getting enough odds to make it a positive EV bet.
The fact that you have a previous bet which now has a substantial positive EV does not affect the EVof any subsequent bet.
As far as your second question, if the few hundred thousand you could lock in by giving up the chance to win the 400,000 is a significant amount of money to you and you would do something with thatfew hundred thousand then it might make sense for you to give up the EV. My guess is if you were a betting $2000 on a future bet at 20 to 1 odds the few hundred thousand dollars although a very nice pay day is probably not a life-changing pay day.
Thanks for the post. Im still wrapping my head around it . You state 'The fact that you have a previous bet which now has a substantial positive EV does not affect the EV of any subsequent bet.' I understand that it doesnt affect the EV of any subsequent individual series bet, but I am looking at the overall scenario of the transaction which is inclusive of all playoff series outcome. Once my team has made it to the playoffs , then I can ensure that my initial bet/risk is a non factor, thus ensuring that I win on the overall scenario without risking and L regardless of what happens throughout the series.
I guess it is more a matter of principle. No, the payouts are not life changing, but the though of a loss when I had guaranteed profits is unsettling. Its like being up on the tables and you are ready to leave the casino with a W, but you get greedy and decide to go back in and wind up losing . Lock the W, and live another day.
In this case for me, I have 1000 on the sixers (as you know) averaged in at 90-1 odds. I have a possible win of 90k if they win it all. I didnt hedge first series against the heat and fortunately, the sixers made it to round two. Now I could hedge the celtics at +400 and ensure a profit. I considered just putting a small amount of 500. This would win 2k if celtics beat sixers. I would at least win something if this happens. If the sixers win, then Im down 1500 going into ECF. Sixers should be favored by a little again. I would then bet enough to cover my prior bets and a little more to guarantee myself a couple grand profit if sixers lose. Now if sixers win again, I have 90k still alive , and Im already in for about 3500 or so. Now I do the same in the championship game. Sixers wont be favored then, but there is still plenty of room for a hedge to guarantee a nice overall profit.
Then there are gamblers like you and me. We let feelings get in the way of the true monetary value of any bet. I know that I feel much better leaving the casino or sports book a winner. So if I am down $20 I may make a bet that I know is negative EV for $25. So I may leave the casino up five dollars and feel good, or leave the casino down $45 and feel the same amount bad as if I had lost $20. So although technically The last bet was not a good one, to me it would feel like it was.
Quote: WatchMeWinthe thought of a loss when I had guaranteed profits is unsettling. .
If you hedge, and your original bet ends up winning, then the thought of the money you lost on that hedge should be even more unsettling. You made a good bet and then artificially lowered the payout. Especially since the hedge was probably not what you considered a good bet or a +EV bet, but was instead just an offsetting bet made out of fear of losing your original bet
Quote: SOOPOOWMW, without quoting your entire post you still don't get the point that there are two types of bettors. There are bettors we refer to as advantage players who kind of make their living by betting. They don't look at it as I'm trying to make a few bucks on this one particular scenario, but rather, if you tally all my bets I want to make money. And not just all the bets revolving around your sixers long term bet. So the next bet, which you are calling a hedge, is one that the advantage player will analyze on its own merit. It is either a good bet or a bad bet and the fact that you have some previous bet that is tied into it is irrelevant.
Then there are gamblers like you and me. We let feelings get in the way of the true monetary value of any bet. I know that I feel much better leaving the casino or sports book a winner. So if I am down $20 I may make a bet that I know is negative EV for $25. So I may leave the casino up five dollars and feel good, or leave the casino down $45 and feel the same amount bad as if I had lost $20. So although technically The last bet was not a good one, to me it would feel like it was.
I understand your point now. Thank you for sharing.
Quote: michael99000If you hedge, and your original bet ends up winning, then the thought of the money you lost on that hedge should be even more unsettling. You made a good bet and then artificially lowered the payout. Especially since the hedge was probably not what you considered a good bet or a +EV bet, but was instead just an offsetting bet made out of fear of losing your original bet
I don't think you can call a preseason bet on the GK to win the Stanley Cup a good bet. A dumb bet that might pay off , but a good bet?
Quote: billryanI don't think you can call a preseason bet on the GK to win the Stanley Cup a good bet. A dumb bet that might pay off , but a good bet?
It’s hard to say. Maybe someone with extensive hockey knowledge saw something in what they had on that team in October. Fluery has some success in Pittsburgh. All they had to determine was that the team had a better than 1 in 200 chance of winning to say it was a good bet. And that doesn’t really require a high degree of certainty.
Quote: billryanI don't think you can call a preseason bet on the GK to win the Stanley Cup a good bet. A dumb bet that might pay off , but a good bet?
If betting $1,000 to win $200,000 wasn’t a good bet, then laying $150,000 to win $1,000 that the Knights wouldn’t win the Cup (which was available in the preseason) must have been a great bet.
Quote: TomGIf betting $1,000 to win $200,000 wasn’t a good bet, then laying $150,000 to win $1,000 that the Knights wouldn’t win the Cup (which was available in the preseason) must have been a great bet.
I understand your point, but that's not accurate. Laying $150,000 before a season starts to win $1000 can never be a good bet. If you put the $150,000 in a 1% interest bearing account, you'd end up with more.
That kind of bet is actually the worst bet you can make in a casino. There's no way to win, and you can lose $150,000!
Quote: WatchMeWin.... but what if in your blackjack comparison you were to lose your initial bet instead of pushing if the dealer pulls over a bj also? This is more of a parallel scenario to the hedge described. Do you risk taking and L?
I would need to know the probabilities of any hypothetical. How about this:
Option 1: 50% chance lose $100, 50% chance win $1000
Option 2: 100% chance win $100
Which do you pick? I would take option 1.
Quote: WizardI would need to know the probabilities of any hypothetical. How about this:
Option 1: 50% chance lose $100, 50% chance win $1000
Option 2: 100% chance win $100
Which do you pick? I would take option 1.
If I can only play once and never again, I take option 2
If it’s a game I can keep playing over and over as much as I want, I take option 1 everytime
Quote: michael99000It’s hard to say. Maybe someone with extensive hockey knowledge saw something in what they had on that team in October. Fluery has some success in Pittsburgh. All they had to determine was that the team had a better than 1 in 200 chance of winning to say it was a good bet. And that doesn’t really require a high degree of certainty.
My nephew bought these tickets to give to his wedding party. I wasn't included.
His brother works for the Islanders. He started as a glorified gofer and has moved up a few times to some sort of hybrid scout/ administrator. He thought the Knights put together an amazing roster but they wouldn't have the depth to handle the long season.
Quote: WizardI would need to know the probabilities of any hypothetical. How about this:
Option 1: 50% chance lose $100, 50% chance win $1000
Option 2: 100% chance win $100
Which do you pick? I would take option 1.
Of course I would choose option 1 with these scenarios.
Quote: michael99000If I can only play once and never again, I take option 2
If it’s a game I can keep playing over and over as much as I want, I take option 1 everytime
Better to take option 1.
Over 1000 sessions, presume you win 50% of the time..
With option 1 you would be up 500k
With option 2 you would only be up 100k
.....and so on and so on.....
Quote: WatchMeWinBetter to take option 1.
Over 1000 sessions, presume you win 50% of the time..
With option 1 you would be up 500k (sorry, up 450k, not 500k)
With option 2 you would only be up 100k
.....and so on and so on.....
Quote: Wizardofoddz123Always Hedge
All of your posts are very well thought out and insightful. I'm sure others along with me will be anxiously awaiting your future plans.
ZCore13
