Gaining an Edge on Coin Flips
A player believes he can gain an edge on this 50/50 game by running a linear progression. He starts by placing a $1 bet on either heads or tails, then increases his wager by $1 on the subsequent bet. Following any loss, he keeps increasing his bet by $1 until he records a win. Then he starts over again at $1.
Unlike with a Martingale progression, he faces no plausible risk of busting. Even if he loses his first 100 flips in the worst string of bad luck ever documented, he would have plenty of room to continue raising before getting anywhere near the $10,000 max.
Yes, he would suffer a massive overall loss in that unlikely situation. But he remains convinced that his system gives him an edge in the long run. His reasoning is that even though he expects to win only 50% of flips, he expects his average bet size on wins to be larger than on losses.
A more typical session will see him place 100 bets and win 50 of them. If his wagers end up ranging from $1 to $10, then he will have some losses and some wins when wagering between $1 and $9 -- but no losses and at least one win at the $10 level. Thus skewed, the total value of his 50 wins will likely exceed the total value of his 50 losses, generating a small profit for the session.
Over the course of many sessions, variance will eventually cause him to lose a $10 bet and raise his bet size. But however high it gets, his top bet size will be a win. The 50% of all bets that result in losses will be distributed among smaller bet sizes. The 50% of all bets that result in wins will contain the biggest bet.
The system cannot guarantee that the average bet size on wins will be higher than on losses (the single worst losing streak the player experiences could result in lots of outlier high-bet losses before the highest-bet win). But if it increases the likelihood of wins having a bigger average weighting than losses, then the player should have a genuine advantage in this 50/50 game - however slight it might be.
It would be interesting to see whether statistical simulations show the player profiting after millions of flips.
He's wrong.Quote: JackSpade
A player believes he can gain an edge on this 50/50 game by running a linear progression.
So what?Quote:
But he remains convinced that his system gives him an edge in the long run. His reasoning is that even though he expects to win only 50% of flips, he expects his average bet size on wins to be larger than on losses.
Quote:It would be interesting to see whether statistical simulations show the player profiting after millions of flips.
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You need to say what his start and end criteria are. Is he going to make a fixed number of wagers? Is he going to stop completely when he's ahead?
Zero need to simulate this, but until you set the parameters, there's even less need.
If his intent is to quit when he's ahead, you can easily provethat he has a massive probability of success. It's not an edge.
https://wizardofvegas.com/member/oncedear/blog/8/#post1370
I would ask you, how many wagers would the player need to make in order for you to be confident that he has no more than a 50% chance of being profitable?
# of tosses, amount lost, amount won, net, probability, contribution
1 0 1 +1 1/2 +1/2
2 1 2 +1 1/4 +1/4
3 3 3 0 1/8 0
4 6 4 -2 1/16 -1/8
5 10 5 -5 1/32 -5/32
6 15 6 -9 1/64 -9/64
7 21 7 -14 1/128 -7/64
8 28 8 -20 1/256 -5/64
9 36 9 -27 1/512 -27/512
10 45 10 -35 1/1024 -35/1024
11 55 11 -44 1/2048 -11/512
12 66 12 -54 1/4096 -27/2048
13 78 13 -65 1/8192 -65/8192
14 91 14 -77 1/16386 -77/16386
15 105 15 -90 1/32772 -45/16386
16 120 16 -104 1/65544 -13/8192
17 136 17 -119 1/131088 -119/131088
18 153 18 -135 1/262176 -135/262176
…
Adding the first 18 items of the ‘contribution’ column gives an EV of just over +0.0006534. Does this mean that your system gives you an edge? NO! Keep adding terms (note the rest will also be negative) until depleting the $10,000… Before you get that far, you’ll see that the EV is zero. Why? Because CHANGING THE BET AMOUNT DOES NOT CHANGE THE RETURN OF THE GAME!!!
The question is whether it changes the average bet size on wins relative to losses.
Suppose that the casino, having analyzed the player's betting patterns, believes that it is being exploited by an advantage player. It threatens to restrict the player to flat betting unless he agrees to end all his progressions on losses, thus ensuring that the casino 'wins' on his biggest bets. Should the player not care?
if he loses 5 bets in a row - 1,2,3,4, 5 and wins the the sixth bet of 6 he will have lost 15 and won 6 for a net loss of 9
how did it benefit him that his biggest bet was a win_____?
whenever he wins a big bet it means that he has lost many smaller bets - and that means a net loss
.
Quote: JackSpade"CHANGING THE BET AMOUNT DOES NOT CHANGE THE RETURN OF THE GAME!!!"
The question is whether it changes the average bet size on wins relative to losses.
Suppose that the casino, having analyzed the player's betting patterns, believes that it is being exploited by an advantage player. It threatens to restrict the player to flat betting unless he agrees to end all his progressions on losses, thus ensuring that the casino 'wins' on his biggest bets. Should the player not care?
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Yes, I understood the question, hence the table… No, the player should not care, nor should the casino, because… (must I write it again?)
Quote: lilredrooster.
if he loses 5 bets in a row - 1,2,3,4, 5 and wins the the sixth bet of 6 he will have lost 15 and won 6 for a net loss of 9
how did it benefit him that his biggest bet was a win_____?
whenever he wins a big bet it means that he has lost many smaller bets - and that means a net loss
.
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He could also win bets 1,2,3,4, lose the 5th, and win the 6th. Over time, he can expect to win 50% of all bets between 1 and 6. Whatever his top bet happens to in any session, number of sessions, or entire lifetime of wagering has an effective 100% chance of resulting in a win given the assumptions set forth in the hypothetical example.
Even without a House Edge it's going to be -EV.Quote: JackSpadeA hypothetical online casino offers a virtual coin flip game that gives players exactly even odds on heads vs. tails; no house edge. Players may wager any amount from $1 to $10,000.
A player believes he can gain an edge on this 50/50 game by running a linear progression. He starts by placing a $1 bet on either heads or tails, then increases his wager by $1 on the subsequent bet. Following any loss, he keeps increasing his bet by $1 until he records a win. Then he starts over again at $1.
Unlike with a Martingale progression, he faces no plausible risk of busting. Even if he loses his first 100 flips in the worst string of bad luck ever documented, he would have plenty of room to continue raising before getting anywhere near the $10,000 max.
Yes, he would suffer a massive overall loss in that unlikely situation. But he remains convinced that his system gives him an edge in the long run. His reasoning is that even though he expects to win only 50% of flips, he expects his average bet size on wins to be larger than on losses.
A more typical session will see him place 100 bets and win 50 of them. If his wagers end up ranging from $1 to $10, then he will have some losses and some wins when wagering between $1 and $9 -- but no losses and at least one win at the $10 level. Thus skewed, the total value of his 50 wins will likely exceed the total value of his 50 losses, generating a small profit for the session.
Over the course of many sessions, variance will eventually cause him to lose a $10 bet and raise his bet size. But however high it gets, his top bet size will be a win. The 50% of all bets that result in losses will be distributed among smaller bet sizes. The 50% of all bets that result in wins will contain the biggest bet.
The system cannot guarantee that the average bet size on wins will be higher than on losses (the single worst losing streak the player experiences could result in lots of outlier high-bet losses before the highest-bet win). But if it increases the likelihood of wins having a bigger average weighting than losses, then the player should have a genuine advantage in this 50/50 game - however slight it might be.
It would be interesting to see whether statistical simulations show the player profiting after millions of flips.
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Why, you ask?
Because there's probably a 20% chance that at some point the casino will screw someone out if their money.
There's usually some kind of transaction free for the player.
There's really not a way to tell if it's actually fair. It could be fair one day, and unfair the next day.
If they require KYC documents that's another risk that your information could be misused
If you are using Crypto could cause unfortunate problems as well.
Is the risk worth the the break even reward?
Quote: JackSpadeA hypothetical online casino offers a virtual coin flip game that gives players exactly even odds on heads vs. tails; no house edge. Players may wager any amount from $1 to $10,000.
A player believes he can gain an edge on this 50/50 game by running a linear progression. He starts by placing a $1 bet on either heads or tails, then increases his wager by $1 on the subsequent bet. Following any loss, he keeps increasing his bet by $1 until he records a win. Then he starts over again at $1.
Unlike with a Martingale progression, he faces no plausible risk of busting. Even if he loses his first 100 flips in the worst string of bad luck ever documented, he would have plenty of room to continue raising before getting anywhere near the $10,000 max.
Yes, he would suffer a massive overall loss in that unlikely situation. But he remains convinced that his system gives him an edge in the long run. His reasoning is that even though he expects to win only 50% of flips, he expects his average bet size on wins to be larger than on losses.
A more typical session will see him place 100 bets and win 50 of them. If his wagers end up ranging from $1 to $10, then he will have some losses and some wins when wagering between $1 and $9 -- but no losses and at least one win at the $10 level. Thus skewed, the total value of his 50 wins will likely exceed the total value of his 50 losses, generating a small profit for the session.
Over the course of many sessions, variance will eventually cause him to lose a $10 bet and raise his bet size. But however high it gets, his top bet size will be a win. The 50% of all bets that result in losses will be distributed among smaller bet sizes. The 50% of all bets that result in wins will contain the biggest bet.
The system cannot guarantee that the average bet size on wins will be higher than on losses (the single worst losing streak the player experiences could result in lots of outlier high-bet losses before the highest-bet win). But if it increases the likelihood of wins having a bigger average weighting than losses, then the player should have a genuine advantage in this 50/50 game - however slight it might be.
It would be interesting to see whether statistical simulations show the player profiting after millions of flips.
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You only get to place a large bet after you have been extraordinarily unlucky and lost a lot of money. If you do sims, you would see that this exactly cancels out the fact that you always win the largest bet that you make.
If your largest bet is $10, then you have just lost $45 on the preceding nine rolls. Winning that $10 bet left you worse off than winning a $1 bet.
Stop wasting time on this sophistry about a hypothetical game that does not exist. Try to learn about the many time tested methods that APs use to gain an advantage.
