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What is value in gambling?
Monday, 15 January 2024
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You may have read about EV (Expected Value) in gambling, it is simply the value; either positive or negative; that is expected for a bet.
So if I offered you a choice between one series of bets with a +0.1 EV (10% edge) and another series of bets with a +0.5 EV (50% edge), which would you choose?
Most people would probably take the +0.5 EV series as it naturally seems the correct thing to do.
But you need to know more before you choose - firstly what if the +0.1 EV series of bets were all at even money ($2) and the +0.5 EV series of bets were all at 100/1 ($101), which is the better series of bets then?
The correct answer is the 10% edge at $2 is better as it can deliver four and a half times higher bank growth/bet than the 50% edge at $101 if you were to utilise the Kelly Criterion for your bet sizing (which you should).
The full Kelly criterion staking for a 10% edge at even money is to bet 10% of your bank and this should deliver (over a large series of bets) expected bank growth of 0.5% per bet. This compares to Kelly staking of 0.5% of your bank for a 50% edge at $101 which would only deliver expected bank growth of 0.11% per bet i.e. four and a half times less.
You would need to more than double your 50% edge to a 115% edge for the 100/1 series of bets to achieve the same bank growth per bet as the 10% edge at even money if you are utilising the Kelly criterion.
The final piece of the puzzle that you need to know before correctly choosing is how many bets are there in each series over a period of time, obviously if there were four and a half times more $101 bets in the same time period then you could choose either series; as bank growth over time would be the same; but in reality you would eventually have difficulty getting set for large bets at $101 and/or achieving that price.
In conclusion maximising wealth from any edge should be the principle aim and to achieve this you need to know what your edge is for each odds range and how many bets can be generated with that edge at each odds range. You also need to manage your risk of ruin effectively and this is typically achieved by using a factor of Kelly instead of full Kelly and by sufficiently testing your edge to ensure it is real and that it can be maintained.
Finally always be aware that a smaller edge at a low price can often hold the most “Value”.
Must read: The benefits of multiple betting services
Also read: Perspective
Ian G
| Strike rate required at various odds ranges to achieve 1% bank growth per bet utilising Full Kelly criterion | |||||||
| Kelly Factor - | 100% | ||||||
| Bets | |||||||
| 1000 | |||||||
| A | B | C | D | E | F | G | I |
| Divi | Odds to 1 | SR | ROI (level Stks) | EV | Full Kelly | E(G) | ELS |
| $1.50 | $0.50 | 73.2% | 10% | 0.10 | 19.6% | 1.00% | 5 |
| $2.00 | $1.00 | 57.1% | 14% | 0.14 | 14.1% | 1.00% | 8 |
| $3.00 | $2.00 | 40.1% | 20% | 0.20 | 10.1% | 1.00% | 13 |
| $4.00 | $3.00 | 31.3% | 25% | 0.25 | 8.3% | 1.00% | 18 |
| $5.00 | $4.00 | 25.8% | 29% | 0.29 | 7.3% | 1.00% | 23 |
| $7.00 | $6.00 | 19.5% | 36% | 0.36 | 6.0% | 1.00% | 32 |
| $9.00 | $8.00 | 15.8% | 42% | 0.42 | 5.3% | 1.00% | 40 |
| $11.00 | $10.00 | 13.4% | 47% | 0.47 | 4.7% | 1.00% | 48 |
| $13.00 | $12.00 | 11.7% | 52% | 0.52 | 4.4% | 1.00% | 55 |
| $17.00 | $16.00 | 9.5% | 61% | 0.61 | 3.8% | 1.00% | 69 |
| $21.00 | $20.00 | 8.1% | 69% | 0.69 | 3.5% | 1.00% | 82 |
| $34.00 | $33.00 | 5.6% | 91% | 0.91 | 2.8% | 1.00% | 119 |
| $51.00 | $50.00 | 4.2% | 115% | 1.15 | 2.3% | 1.00% | 161 |
| $101.00 | $100.00 | 2.7% | 171% | 1.71 | 1.7% | 1.00% | 254 |
| $501.00 | $500.00 | 1.1% | 456% | 4.56 | 0.9% | 1.00% | 619 |
| Strike rate required at various odds ranges to achieve 0.5% bank growth per bet utilising Full Kelly criterion | Bets | ||||||
| 1000 | |||||||
| A | B | C | D | E | F | G | I |
| Divi | Odds to 1 | SR | ROI (level Stks) | EV | Full Kelly | E(G) | ELS |
| $1.50 | $0.50 | 71.3% | 7% | 0.07 | 13.9% | 0.50% | 6 |
| $2.00 | $1.00 | 55.0% | 10% | 0.10 | 10.0% | 0.50% | 9 |
| $3.00 | $2.00 | 38.1% | 14% | 0.14 | 7.1% | 0.50% | 14 |
| $4.00 | $3.00 | 29.4% | 18% | 0.18 | 5.9% | 0.50% | 20 |
| $5.00 | $4.00 | 24.1% | 20% | 0.20 | 5.1% | 0.50% | 25 |
| $7.00 | $6.00 | 17.9% | 25% | 0.25 | 4.2% | 0.50% | 35 |
| $9.00 | $8.00 | 14.4% | 29% | 0.29 | 3.7% | 0.50% | 45 |
| $11.00 | $10.00 | 12.1% | 33% | 0.33 | 3.3% | 0.50% | 54 |
| $13.00 | $12.00 | 10.5% | 36% | 0.36 | 3.0% | 0.50% | 62 |
| $17.00 | $16.00 | 8.4% | 42% | 0.42 | 2.6% | 0.50% | 79 |
| $21.00 | $20.00 | 7.0% | 48% | 0.48 | 2.4% | 0.50% | 95 |
| $34.00 | $33.00 | 4.8% | 62% | 0.62 | 1.9% | 0.50% | 141 |
| $51.00 | $50.00 | 3.5% | 78% | 0.78 | 1.6% | 0.50% | 194 |
| $101.00 | $100.00 | 2.1% | 115% | 1.15 | 1.2% | 0.50% | 321 |
| $501.00 | $500.00 | 0.8% | 296% | 2.96 | 0.6% | 0.50% | 870 |
| +0.5 EV at $101 | |||||||
| $101.00 | $100.00 | 1.5% | 50% | 0.50 | 0.5% | 0.11% | 460 |
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